log_database.m

Magma V2.26-10    Thu Mar 24 2022 16:10:35 on LEGENDRE [Seed = 290427431]

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Type ? for help.  Type <Ctrl>-D to quit.
computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<2, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1]) >
quotient genus = 1
MatrixGroup<2, RationalField() |
    DiagonalMatrix(RationalField(), [1, -1]) >
quotient genus = 1
making ShimDB object
<[ 1, 2 ], Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 - 213*x - 1257
over Rational Field, 1, <0, "C_1">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + x*y + y = x^3
- x^2 - 213*x - 1257 over Rational Field
with equations :
-7/4*X^3 - 169/4*X*T^2
3/8*X^3 + 169/8*X*T^2 - 169/8*Y*T^2
X^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        -$.2,
        $.3
    ]
]>
<[ 1, 13 ], Elliptic Curve defined by y^2 + x*y + y = x^3 - 5*x - 8 over
Rational Field, 1, <0, "C_3">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + x*y + y = x^3
- 5*x - 8 over Rational Field
with equations :
-1/2*X^2 + 3/2*T^2
1/4*X^2 + 1/4*Y*T - 5/4*T^2
T^2, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>
<[ 1, 26 ], Curve over Rational Field defined by
0, 0, 0, 0, 0>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    ScalarMatrix(RationalField(), 3, -1) >
quotient genus >= 2
making ShimDB object
<[ 1, 7 ], Elliptic Curve defined by y^2 + y = x^3 + x^2 + 9*x + 1 over Rational
Field, 1, <0, "C_3">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + y = x^3 + x^2
+ 9*x + 1 over Rational Field
with equations :
-3*X^4 - 22*X^2*T^2 - 7*T^4
-1/2*X^4 - 7*X^2*T^2 + 5/2*Y*T^3 - 49/2*T^4
X^4 + 14*X^2*T^2 + 49*T^4, [
    [
        -$.1,
        $.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 35 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 5 ], Hyperelliptic Curve defined by y^2 + (x^2 + 1)*y = -7*x^5 + x^4 + x^3
    + x^2 + 5*x - 4 over Rational Field, 2, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 + (x^2 + 1)*y = -7*x^5 + x^4 + x^3 + x^2 +
    5*x - 4 over Rational Field
with equations :
1/4*X^2*T^2 + 3/4*T^4
-1/32*X^4*T^8 - 3/16*X^2*T^10 - 1/32*X*Y*T^10 - 25/32*T^12
T^4, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<2, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1]) >
quotient genus = 1
MatrixGroup<2, RationalField() |
    DiagonalMatrix(RationalField(), [1, -1]) >
quotient genus = 1
making ShimDB object
<[ 1, 2 ], Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 70*x - 279 over
Rational Field, 1, <0, "C_1">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + x*y + y = x^3
+ x^2 - 70*x - 279 over Rational Field
with equations :
-29/4*X^3 - 19/4*X*T^2
25/8*X^3 + 19/8*X*T^2 - 19/8*Y*T^2
X^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        -$.2,
        $.3
    ]
]>
<[ 1, 19 ], Elliptic Curve defined by y^2 + x*y + y = x^3 + 9*x + 90 over
Rational Field, 1, <0, "C_3">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + x*y + y = x^3
+ 9*x + 90 over Rational Field
with equations :
-4*X^2 - 5*T^2
2*X^2 + 2*Y*T + 2*T^2
T^2, [
    [
        -$.1,
        $.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 38 ], Curve over Rational Field defined by
0, 0, 0, 0, 0>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, 1, 0, -1, 0, 1, 0, 0 ]) >
quotient genus = 1
quotient genus >= 2
making ShimDB object
<[ 1, 13 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
7*x[1]^2 + 30*x[1]*x[2] + 49*x[2]^2 + 42*x[2]*x[3] + 19*x[3]^2 + x[4]^2, 1, <0, "C_2^2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
7*x[1]^2 + 30*x[1]*x[2] + 49*x[2]^2 + 42*x[2]*x[3] + 19*x[3]^2 + x[4]^2
with equations :
X^4 - 2*X^2*T^2 + T^4
-X^3*T + X*T^3
X^2*T^2
Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        $.2,
        $.1
    ]
]>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -2*x^6 - 3*x^5 -
    8*x^4 + 3*x^3 + x^2 + 6*x - 4 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -2*x^6 - 3*x^5 -
    8*x^4 + 3*x^3 + x^2 + 6*x - 4 over Rational Field
with equations :
X^2*T^4 - X*T^5 - T^6
-1/2*X^6*T^12 + 3/2*X^5*T^13 - 3*X^3*T^15 - 1/2*X^2*Y*T^15 + 3/2*X*T^17 -
    1/2*Y*T^17 + 1/2*T^18
X*T^5, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        -$.2,
        $.1
    ]
]>
<[ 1, 39 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
making ShimDB object
<[ 1, 51 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 17 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^6 - 15*x^5 -
    39*x^4 - 21*x^3 + 19*x^2 - 3*x over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^6 -
    15*x^5 - 39*x^4 - 21*x^3 + 19*x^2 - 3*x over Rational Field
with equations :
-X^2*T^4
17/32*X^6*T^12 - 1/16*X^4*T^14 + 1/32*X^2*T^16 - 1/32*X*Y*T^16
1/4*X^2*T^4 - 1/4*T^6, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        -$.2,
        $.3
    ]
]>
<[ 1, 3 ], Elliptic Curve defined by y^2 + y = x^3 + x^2 - 59*x - 196 over
Rational Field, 1, <0, "C_1">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + y = x^3 + x^2
- 59*x - 196 over Rational Field
with equations :
-27*X^4 - 94*X^2*T^2 - 39*T^4
-1/2*X^4 - 3*X^2*T^2 + 17/2*Y*T^3 - 9/2*T^4
X^4 + 6*X^2*T^2 + 9*T^4, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, 1, 0, -1, 0, 1, 0, 0 ]) >
quotient genus = 1
quotient genus >= 2
making ShimDB object
<[ 1, 55 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 5 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
3*x[1]^2 + 2*x[1]*x[2] + 9*x[2]^2 - 2*x[2]*x[3] + 3*x[3]^2 + x[4]^2, 1, <0, "C_2^2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
3*x[1]^2 + 2*x[1]*x[2] + 9*x[2]^2 - 2*x[2]*x[3] + 3*x[3]^2 + x[4]^2
with equations :
X^4 - 2*X^2*T^2 + T^4
-X^3*T + X*T^3
X^2*T^2
Y*T^3, [
    [
        -$.3,
        $.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 11 ], Hyperelliptic Curve defined by y^2 + (x^3 + x^2 + x)*y = -x^6 -
    6*x^4 + x^3 - 10*x^2 - 2*x - 3 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x^2 + x)*y = -x^6
    - 6*x^4 + x^3 - 10*x^2 - 2*x - 3 over Rational Field
with equations :
X^2*T^4 - T^6
-1/2*X^6*T^12 - 1/2*X^5*T^13 + X^4*T^14 + X^3*T^15 - 1/2*X^2*Y*T^15 - X^2*T^16 -
    1/2*X*T^17 - 1/2*Y*T^17 + 1/2*T^18
X*T^5, [
    [
        -$.3,
        -$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
non-hyperelliptic case
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
quotient genus >= 2
making ShimDB object
<[ 1, 57 ], Elliptic Curve defined by y^2 + y = x^3 - x^2 - 2*x + 2 over
Rational Field, 1, <1, "C_1">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + y = x^3 - x^2
- 2*x + 2 over Rational Field
with equations :
17/15*Z1^6 - 32/135*Y1^2*Z1^2*T1^2 - 365/54*Z1^4*T1^2 - 608/1215*Y1^2*T1^4 -
    28348/1215*Z1^2*T1^4 - 6859/810*T1^6
-1/2*Z1^6 + 37/45*Y1*Z1^4*T1 + 19/180*Z1^4*T1^2 - 112/405*Y1^3*T1^3 -
    3854/405*Y1*Z1^2*T1^3 + 2888/405*Z1^2*T1^4 + 48013/4860*T1^6
Z1^6 - 19/90*Z1^4*T1^2 - 5776/405*Z1^2*T1^4 - 48013/2430*T1^6, [
    [
        X1,
        Y1,
        -Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 19 ], Conic over Rational Field defined by
256*$.1^2 + 8100*$.2^2 + 11392*$.1*$.3 + 132811*$.3^2, 0, 0, 0, 0>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^6 + 9*x^5 -
    13*x^4 - 6*x^3 + 12*x^2 - 6*x - 1 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^6 +
    9*x^5 - 13*x^4 - 6*x^3 + 12*x^2 - 6*x - 1 over Rational Field
with equations :
-1/320*Z1^4*T1^6 + 1/180*Y1^2*T1^8 + 311/2880*Z1^2*T1^8 + 19/180*T1^10
-1/524288*Z1^10*T1^20 + 1/294912*Y1^2*Z1^6*T1^22 + 1/32768*Y1*Z1^7*T1^22 +
    19/368640*Z1^8*T1^22 - 157/4423680*Y1^2*Z1^4*T1^24 -
    133/327680*Y1*Z1^5*T1^24 - 378931/1415577600*Z1^6*T1^24 +
    30457/265420800*Y1^2*Z1^2*T1^26 + 17689/9830400*Y1*Z1^3*T1^26 +
    1027273/21233664000*Z1^4*T1^26 - 17689/165888000*Y1^2*T1^28 -
    2352637/884736000*Y1*Z1*T1^28 + 22821337/21233664000*Z1^2*T1^28 +
    20501551/21233664000*T1^30
-1/640*Z1^4*T1^6 + 1/360*Y1^2*T1^8 + 131/5760*Z1^2*T1^8 + 551/2880*T1^10, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        -Y1,
        -Z1,
        T1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<2, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1]) >
quotient genus = 1
MatrixGroup<2, RationalField() |
    DiagonalMatrix(RationalField(), [1, -1]) >
quotient genus = 1
making ShimDB object
<[ 1, 2 ], Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 455*x - 3951
over Rational Field, 1, <0, "C_1">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + x*y + y = x^3
+ x^2 - 455*x - 3951 over Rational Field
with equations :
-147/8*X^3 - 841/8*X*T^2
139/16*X^3 + 841/16*X*T^2 - 841/32*Y*T^2
X^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        -$.2,
        $.3
    ]
]>
<[ 1, 29 ], Curve over Rational Field defined by
0, 0, 0, 0, 0>
<[ 1, 58 ], Elliptic Curve defined by y^2 + x*y = x^3 - x^2 - x + 1 over
Rational Field, 1, <1, "C_1">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + x*y = x^3 -
x^2 - x + 1 over Rational Field
with equations :
-1/8*X^2 - 11/8*T^2
1/16*X^2 + 1/32*Y*T + 11/16*T^2
T^2, [
    [
        -$.1,
        $.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
quotient genus >= 2
making ShimDB object
<[ 1, 2 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
256*x[1]^2 - 396*x[1]*x[2] + 360*x[2]^2 - 172*x[2]*x[3] + 32*x[3]^2 + x[4]^2, 1,
<0, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
256*x[1]^2 - 396*x[1]*x[2] + 360*x[2]^2 - 172*x[2]*x[3] + 32*x[3]^2 + x[4]^2
with equations :
X^4
-X^2*T^2
T^4
2*Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>
<[ 1, 62 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 31 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 2*x^5 - x^4 - x^3
    - 2*x^2 + x + 5 over Rational Field, 2, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 2*x^5 - x^4 - x^3 - 2*x^2 + x
    + 5 over Rational Field
with equations :
X^2*T^2 + T^4
1/2*X^4*T^8 + 1/2*X^2*T^10 - 1/2*X*Y*T^10
-X^2*T^2, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
making ShimDB object
<[ 1, 69 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 23 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 3*x^5 - 11*x^4 +
    13*x^3 + 13*x^2 - 1 over Rational Field, 2, -1, Mapping from: Crv: top_curve
to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 3*x^5 - 11*x^4 + 13*x^3 +
    13*x^2 - 1 over Rational Field
with equations :
-1/36*X^2*T^4 + 1/4*T^6
5/23328*X^6*T^12 - 1/432*X^4*T^14 + 1/288*X^2*T^16 - 1/2592*X*Y*T^16
-1/9*X^2*T^4, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        -$.2,
        $.3
    ]
]>
<[ 1, 3 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
972*x[1]^2 + 5072*x[1]*x[2] + 2664*x[2]^2 - 9072*x[2]*x[3] + 8748*x[3]^2 +
    x[4]^2, 1, <0, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
972*x[1]^2 + 5072*x[1]*x[2] + 2664*x[2]^2 - 9072*x[2]*x[3] + 8748*x[3]^2 +
    x[4]^2
with equations :
X^4
-X^2*T^2
T^4
2*Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 74 ], Curve over Rational Field defined by
0, 0, 0, 0, 0>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -6*x^6 - 16*x^5 -
    8*x^4 - 8*x^3 - 7*x^2 + 17*x - 5 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -6*x^6 -
    16*x^5 - 8*x^4 - 8*x^3 - 7*x^2 + 17*x - 5 over Rational Field
with equations :
-1/8*X^2*T^4 + 5/8*T^6
1/512*X^6*T^12 - 3/512*X^4*T^14 - 13/512*X^2*T^16 - 1/128*X*Y*T^16 + 15/512*T^18
-1/8*X^2*T^4 - 3/8*T^6, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        -$.2,
        $.3
    ]
]>
<[ 1, 37 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -x^6 + x^5 +
    2*x^4 - 4*x^3 - x^2 + 4*x over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -x^6 + x^5 +
    2*x^4 - 4*x^3 - x^2 + 4*x over Rational Field
with equations :
T^4
-1/128*X^4*T^8 + 9/64*X^2*T^10 - 1/128*Y*T^11 - 65/128*T^12
-1/8*X^2*T^2 + 5/8*T^4, [
    [
        -$.1,
        $.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 86 ], Curve over Rational Field defined by
0, 0, 0, 0, 0>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -x^6 - 5*x^5 - x^4
    + 10*x^3 - 24*x^2 - 26*x - 6 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -x^6 - 5*x^5 -
    x^4 + 10*x^3 - 24*x^2 - 26*x - 6 over Rational Field
with equations :
-1/8*X^2*T^4 - 3/8*T^6
3/512*X^6*T^12 + 7/512*X^4*T^14 - 7/512*X^2*T^16 - 1/128*X*Y*T^16 - 3/512*T^18
3/8*X^2*T^4 + 1/8*T^6, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        -$.2,
        $.3
    ]
]>
<[ 1, 43 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 2*x^6 - 2*x^5 -
    11*x^4 + 6*x^3 + 20*x^2 - 7*x - 11 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 2*x^6 -
    2*x^5 - 11*x^4 + 6*x^3 + 20*x^2 - 7*x - 11 over Rational Field
with equations :
-1/4*X^2*T^4 + 1/4*T^6
3/512*X^6*T^12 + 7/512*X^4*T^14 - 7/512*X^2*T^16 - 1/128*Y*T^17 - 3/512*T^18
-1/8*X^2*T^4 - 3/8*T^6, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 29 ], Hyperelliptic Curve defined by y^2 + (x^3 + x^2 + 1)*y = 3*x^8 +
    18*x^7 + 70*x^6 + 93*x^5 - 36*x^4 - 81*x^3 + 23*x^2 + 14*x - 5 over Rational
Field, 3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2
+ (x^3 + x^2 + 1)*y = 3*x^8 + 18*x^7 + 70*x^6 + 93*x^5 - 36*x^4 - 81*x^3 +
    23*x^2 + 14*x - 5 over Rational Field
with equations :
1/4*X^2*T^6 - 1/4*T^8
-11/256*X^8*T^24 - 15/128*X^6*T^26 - 11/64*X^4*T^28 - 17/128*X^2*T^30 +
    1/128*X*Y*T^30 - 9/256*T^32
1/2*X^2*T^6 + 1/2*T^8, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^3 + x + 1)*y = -x^6 - 7*x^4 +
    16*x^3 + 5*x^2 - 16*x - 4 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x + 1)*y = -x^6 - 7*x^4
    + 16*x^3 + 5*x^2 - 16*x - 4 over Rational Field
with equations :
-3/4*X^2*T^4 - 1/4*T^6
47/128*X^6*T^12 + 79/128*X^4*T^14 + 53/128*X^2*T^16 - 1/128*Y*T^17 + 13/128*T^18
-1/2*X^2*T^4 - 1/2*T^6, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>
<[ 1, 87 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>

computing GYData
making data-quotient list
non-hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 93 ], Hyperelliptic Curve defined by y^2 + (x^3 + x + 1)*y = x^3 + x^2 -
    2*x over Rational Field, 2, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 + (x^3 + x + 1)*y = x^3 + x^2 - 2*x over
Rational Field
with equations :
-1/1664*Z1^6*T1^10 - 59/7488*Z1^4*T1^12 - 1/234*Y1^2*T1^14 + 359/7488*Z1^2*T1^14
    - 155/1664*T1^16
-3/54525952*Z1^16*T1^32 - 2827/2126512128*Z1^14*T1^34 - 1/524288*Y1*Z1^12*T1^35
    - 1/2555904*Y1^2*Z1^10*T1^36 - 2096227/82933972992*Z1^12*T1^36 -
    111/3407872*Y1*Z1^10*T1^37 - 131/49840128*Y1^2*Z1^8*T1^38 -
    765965/2126512128*Z1^10*T1^38 - 6525/22151168*Y1*Z1^8*T1^39 -
    2209/323960832*Y1^2*Z1^6*T1^40 - 129362507/41466986496*Z1^8*T1^40 -
    229585/143982592*Y1*Z1^6*T1^41 + 7103/161980416*Y1^2*Z1^4*T1^42 -
    119730743/6911164416*Z1^6*T1^42 - 202275/35995648*Y1*Z1^4*T1^43 +
    2573/10123776*Y1^2*Z1^2*T1^44 - 626707687/10366746624*Z1^4*T1^44 -
    106671/8998912*Y1*Z1^2*T1^45 + 6727/10123776*Y1^2*T1^46 -
    20499091/161980416*Z1^2*T1^46 - 29791/2249728*Y1*T1^47 -
    8847927/71991296*T1^48
-1/1664*Z1^6*T1^10 + 175/7488*Z1^4*T1^12 - 1/234*Y1^2*T1^14 +
    1691/7488*Z1^2*T1^14 + 837/1664*T1^16, [
    [
        X1,
        Y1,
        -Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^3 + x^2 + 1)*y = -x^8 + 2*x^7
    - 10*x^6 - 29*x^5 - 21*x^4 - 35*x^3 - 28*x^2 - 9*x - 13 over Rational Field,
3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3
    + x^2 + 1)*y = -x^8 + 2*x^7 - 10*x^6 - 29*x^5 - 21*x^4 - 35*x^3 - 28*x^2 -
    9*x - 13 over Rational Field
with equations :
-4/2197*Z1^6*T1^18 + 7147/421824*Z1^4*T1^20 - 29/6591*Y1^2*T1^22 +
    21935/105456*Z1^2*T1^22 + 72075/140608*T1^24
-1923/80980417183744*Z1^24*T1^72 + 2547/5061276073984*Y1*Z1^21*T1^74 -
    205817/160379185594368*Z1^22*T1^74 - 67/1897978527744*Y1^2*Z1^18*T1^76 -
    203793/427677828251648*Y1*Z1^19*T1^76 -
    937658095/41057071512158208*Z1^20*T1^76 + 57/39541219328*Y1^3*Z1^15*T1^78 -
    55997/26729864265728*Y1^2*Z1^16*T1^78 -
    1206345873/5559811767271424*Y1*Z1^17*T1^78 -
    175848797929/1156440847592456192*Z1^18*T1^78 +
    366453/13364932132864*Y1^3*Z1^13*T1^80 -
    364047/8224573620224*Y1^2*Z1^14*T1^80 -
    8919432549/2258673530454016*Y1*Z1^15*T1^80 +
    54571984770401/90202386112211582976*Z1^16*T1^80 +
    23496939/86872058863616*Y1^3*Z1^11*T1^82 -
    55567208887/108416329461792768*Y1^2*Z1^12*T1^82 -
    72582891141849/1879216377337741312*Y1*Z1^13*T1^82 +
    6222055245728425/293157754864687644672*Z1^14*T1^82 +
    924844665/564668382613504*Y1^3*Z1^9*T1^84 -
    901084416339/234902047167217664*Y1^2*Z1^10*T1^84 -
    232463075368227/939608188668870656*Y1*Z1^11*T1^84 +
    83182104025308797/390877006486250192896*Z1^12*T1^84 +
    24185849265/3670344486987776*Y1^3*Z1^7*T1^86 -
    29942955961777/1526863306586914816*Y1^2*Z1^8*T1^86 -
    6753705488113041/6107453226347659264*Y1*Z1^9*T1^86 +
    762296257922516389/586315509729375289344*Z1^10*T1^86 +
    15795490419/917586121746944*Y1^3*Z1^5*T1^88 -
    159491981888639/2290294959880372224*Y1^2*Z1^6*T1^88 -
    10638168878328321/3053726613173829632*Y1*Z1^7*T1^88 +
    1592202233678457919/293157754864687644672*Z1^8*T1^88 +
    6290535903/229396530436736*Y1^3*Z1^3*T1^90 -
    31809671986239/190857913323364352*Y1^2*Z1^4*T1^90 -
    5756350263882963/763431653293457408*Y1*Z1^5*T1^90 +
    774216068516500953/48859625810781274112*Z1^6*T1^90 +
    1115643159/57349132609184*Y1^3*Z1*T1^92 -
    11809633018203/47714478330841088*Y1^2*Z1^2*T1^92 -
    1960472767362111/190857913323364352*Y1*Z1^3*T1^92 +
    384038339642368011/12214906452695318528*Z1^4*T1^92 -
    2064847963203/11928619582710272*Y1^2*T1^94 -
    332337290898303/47714478330841088*Y1*Z1*T1^94 +
    118321334274328839/3053726613173829632*Z1^2*T1^94 +
    17509495334680287/763431653293457408*T1^96
89/35152*Z1^6*T1^18 + 2367/70304*Z1^4*T1^20 + 2/2197*Y1^2*T1^22 +
    1229/8788*Z1^2*T1^22 + 25947/70304*T1^24, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        -Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 31 ], Conic over Rational Field defined by
$.1^2 + 13689/177373*$.2^2 + 37312/177373*$.1*$.3 + 4096/177373*$.3^2, 0, 0, 0,
0>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
quotient genus >= 2
making ShimDB object
<[ 1, 94 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 2 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
32*x[1]^2 + 276*x[1]*x[2] + 936*x[2]^2 + 1524*x[2]*x[3] + 1024*x[3]^2 + x[4]^2,
1, <0, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
32*x[1]^2 + 276*x[1]*x[2] + 936*x[2]^2 + 1524*x[2]*x[3] + 1024*x[3]^2 + x[4]^2
with equations :
X^4
-X^2*T^2
T^4
2*Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>
<[ 1, 47 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -2*x^5 - 3*x^4 -
    x^3 - 2*x^2 + 7*x - 3 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -2*x^5 - 3*x^4 -
    x^3 - 2*x^2 + 7*x - 3 over Rational Field
with equations :
X^2*T^2 - 2*T^4
-1/2*X^4*T^8 + 3/2*X^2*T^10 - 1/2*X*Y*T^10 - T^12
T^4, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 95 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 19 ], Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3 + x^2 + x)*y =
-2*x^10 + 6*x^9 - 30*x^8 + 64*x^7 - 149*x^6 + 201*x^5 - 266*x^4 + 187*x^3 -
    132*x^2 + 14*x - 43 over Rational Field, 4, -1, Mapping from: Crv: top_curve
to Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3 + x^2 + x)*y = -2*x^10
    + 6*x^9 - 30*x^8 + 64*x^7 - 149*x^6 + 201*x^5 - 266*x^4 + 187*x^3 - 132*x^2
    + 14*x - 43 over Rational Field
with equations :
X^2*T^8 - T^10
-1/2*X^10*T^40 + 1/2*X^9*T^41 + 2*X^8*T^42 - 3/2*X^7*T^43 - 4*X^6*T^44 +
    2*X^5*T^45 + 4*X^4*T^46 - 3/2*X^3*T^47 + 1/2*X^2*Y*T^47 - 2*X^2*T^48 +
    1/2*X*T^49 + 1/2*Y*T^49 + 1/2*T^50
-X*T^9, [
    [
        -$.3,
        -$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 5 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^3 + x^2 + x + 1)*y =
    -2*x^8 + 6*x^7 - 23*x^6 + 38*x^5 - 60*x^4 + 45*x^3 - 31*x^2 + 3*x - 11 over
Rational Field, 3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve
defined by y^2 + (x^4 + x^3 + x^2 + x + 1)*y = -2*x^8 + 6*x^7 - 23*x^6 + 38*x^5
    - 60*x^4 + 45*x^3 - 31*x^2 + 3*x - 11 over Rational Field
with equations :
X^2*T^6 - T^8
-1/2*X^8*T^24 + 1/2*X^7*T^25 + 3/2*X^6*T^26 - X^5*T^27 - 5/2*X^4*T^28 + X^3*T^29
    + 3/2*X^2*T^30 - 1/2*X*T^31 + 1/2*Y*T^31 - 1/2*T^32
-X*T^7, [
    [
        -$.3,
        $.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 37 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^3 + x^2 + x + 1)*y =
    -x^8 - 5*x^7 - 10*x^6 - 10*x^5 - 9*x^4 - 7*x^3 - 4*x^2 - 2*x - 1 over
Rational Field, 3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve
defined by y^2 + (x^4 + x^3 + x^2 + x + 1)*y = -x^8 - 5*x^7 - 10*x^6 - 10*x^5 -
    9*x^4 - 7*x^3 - 4*x^2 - 2*x - 1 over Rational Field
with equations :
1/3*X^2*T^6 + 1/3*X*T^7 - 1/3*T^8
-5/162*X^8*T^24 + 5/81*X^7*T^25 - 5/81*X^6*T^26 - 5/162*X^5*T^27 +
    19/162*X^4*T^28 + 5/162*X^3*T^29 - 5/81*X^2*T^30 - 5/81*X*T^31 + 1/54*Y*T^31
    - 5/162*T^32
1/3*X^2*T^6 - 2/3*X*T^7 - 1/3*T^8, [
    [
        -$.3,
        $.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 111 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3 + x^2 + x)*y =
-4*x^10 + 4*x^9 - 17*x^8 + 28*x^7 - 42*x^6 + 61*x^5 - 73*x^4 + 57*x^3 - 60*x^2 +
    33*x - 6 over Rational Field, 4, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3 + x^2 + x)*y = -4*x^10 +
    4*x^9 - 17*x^8 + 28*x^7 - 42*x^6 + 61*x^5 - 73*x^4 + 57*x^3 - 60*x^2 + 33*x
    - 6 over Rational Field
with equations :
1/3*X^2*T^8 - 2/3*X*T^9 - 1/3*T^10
-1/486*X^10*T^40 + 2/243*X^9*T^41 - 23/486*X^8*T^42 + 55/486*X^7*T^43 -
    1/162*X^6*T^44 - 28/243*X^5*T^45 + 1/162*X^4*T^46 + 55/486*X^3*T^47 +
    1/54*X^2*Y*T^47 + 23/486*X^2*T^48 + 2/243*X*T^49 + 1/54*Y*T^49 + 1/486*T^50
-1/3*X^2*T^8 - 1/3*X*T^9 + 1/3*T^10, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        -$.2,
        $.1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 119 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 17 ], Hyperelliptic Curve defined by y^2 + (x^6 + x^4 + x^3 + 1)*y =
    -3*x^12 + 2*x^11 + 20*x^10 - 33*x^8 + 31*x^7 + 64*x^6 - 47*x^5 - 55*x^4 +
    50*x^3 + 21*x^2 - 34*x - 13 over Rational Field, 5, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^6 + x^4 + x^3 + 1)*y =
    -3*x^12 + 2*x^11 + 20*x^10 - 33*x^8 + 31*x^7 + 64*x^6 - 47*x^5 - 55*x^4 +
    50*x^3 + 21*x^2 - 34*x - 13 over Rational Field
with equations :
1/4*X^2*T^10 + 3/4*T^12
-1/4096*X^12*T^60 - 1/512*X^10*T^62 - 89/4096*X^8*T^64 - 35/512*X^6*T^66 -
    579/4096*X^4*T^68 - 21/128*X^2*T^70 - 1/2048*X*Y*T^70 - 419/4096*T^72
-1/4*X^2*T^10 + 1/4*T^12, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        -$.2,
        $.3
    ]
]>
<[ 1, 7 ], Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^2 + x + 1)*y =
    -3*x^10 + 3*x^9 + 5*x^8 - x^7 - 17*x^6 - 2*x^5 + 18*x^4 + 6*x^3 - 12*x^2 -
    9*x + 4 over Rational Field, 4, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^2 + x + 1)*y = -3*x^10 +
    3*x^9 + 5*x^8 - x^7 - 17*x^6 - 2*x^5 + 18*x^4 + 6*x^3 - 12*x^2 - 9*x + 4
over Rational Field
with equations :
1/4*X^2*T^8 + 3/4*T^10
-5/2048*X^10*T^40 - 23/2048*X^8*T^42 - 65/1024*X^6*T^44 - 159/1024*X^4*T^46 -
    393/2048*X^2*T^48 + 1/2048*Y*T^49 - 155/2048*T^50
1/4*X^2*T^8 - 1/4*T^10, [
    [
        -$.1,
        $.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 134 ], Curve over Rational Field defined by
0, 0, 0, 0, 0>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^3 + x^2)*y = -19*x^8 + 53*x^7
    + 21*x^6 - 143*x^5 + 5*x^4 + 143*x^3 + 5*x^2 - 56*x - 16 over Rational
Field, 3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2
+ (x^3 + x^2)*y = -19*x^8 + 53*x^7 + 21*x^6 - 143*x^5 + 5*x^4 + 143*x^3 + 5*x^2
    - 56*x - 16 over Rational Field
with equations :
-1/2*X^2*T^5 - 1/2*X*T^6 - 1/2*T^7
-1/16*X^7*T^21 - 5/16*X^6*T^22 - 5/8*X^5*T^23 - 13/16*X^4*T^24 - 5/8*X^3*T^25 -
    5/16*X^2*T^26 - 1/16*X*Y*T^26 - 1/16*X*T^27 - 1/16*Y*T^27
-X*T^6, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        $.3,
        $.2,
        $.1
    ]
]>
<[ 1, 67 ], Hyperelliptic Curve defined by y^2 + (x^3 + x^2)*y = 2*x^8 - 2*x^7 -
    13*x^6 + 14*x^5 + 20*x^4 - 35*x^3 + 13*x^2 + 32*x - 32 over Rational Field,
3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3
    + x^2)*y = 2*x^8 - 2*x^7 - 13*x^6 + 14*x^5 + 20*x^4 - 35*x^3 + 13*x^2 + 32*x
    - 32 over Rational Field
with equations :
-1/2*X^2*T^5 + 3/2*X*T^6 - 1/2*T^7
-1/16*X^7*T^21 + 7/16*X^6*T^22 - 9/8*X^5*T^23 + 23/16*X^4*T^24 - 9/8*X^3*T^25 +
    7/16*X^2*T^26 + 1/16*X*Y*T^26 - 1/16*X*T^27 - 1/16*Y*T^27
1/2*X^2*T^5 - 1/2*X*T^6 + 1/2*T^7, [
    [
        $.3,
        -$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 73 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -x^8 + x^7 - x^6
    + 5*x^5 - x^4 + 5*x^3 - 11*x^2 - 3*x - 11 over Rational Field, 3, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y
= -x^8 + x^7 - x^6 + 5*x^5 - x^4 + 5*x^3 - 11*x^2 - 3*x - 11 over Rational Field
with equations :
X*T^6
-1/16*X^7*T^21 + 3/16*X^6*T^22 - 1/4*X^5*T^23 - 1/16*X^4*T^24 + 1/4*X^3*T^25 +
    3/16*X^2*T^26 + 1/16*X*T^27 + 1/16*Y*T^27
1/2*X^2*T^5 - 1/2*X*T^6 - 1/2*T^7, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        $.2,
        $.1
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^2)*y = -5*x^10 + x^9 -
    4*x^8 + 26*x^7 + 14*x^6 + 43*x^5 - 36*x^4 - 38*x^3 - 110*x^2 - 56*x - 44
over Rational Field, 4, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve
defined by y^2 + (x^4 + x^2)*y = -5*x^10 + x^9 - 4*x^8 + 26*x^7 + 14*x^6 +
    43*x^5 - 36*x^4 - 38*x^3 - 110*x^2 - 56*x - 44 over Rational Field
with equations :
X*T^7
-1/16*X^8*T^32 + 3/16*X^7*T^33 - 1/4*X^6*T^34 - 1/16*X^5*T^35 + 1/4*X^4*T^36 +
    3/16*X^3*T^37 + 1/16*X^2*Y*T^37 + 1/16*X^2*T^38 + 1/16*Y*T^39
1/2*X^2*T^6 - 1/2*X*T^7 - 1/2*T^8, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        -$.2,
        $.1
    ]
]>
<[ 1, 146 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 53 ], Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3 + x^2 + 1)*y =
3*x^11 + 25*x^10 - 46*x^9 - 483*x^8 + 571*x^7 + 1063*x^6 - 286*x^5 - 1361*x^4 +
    1221*x^3 - 437*x^2 + 73*x - 5 over Rational Field, 5, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3 + x^2 + 1)*y
= 3*x^11 + 25*x^10 - 46*x^9 - 483*x^8 + 571*x^7 + 1063*x^6 - 286*x^5 - 1361*x^4
    + 1221*x^3 - 437*x^2 + 73*x - 5 over Rational Field
with equations :
1/4*X^2*T^10 - 1/4*T^12
-1109/2048*X^12*T^60 + 197/2048*X^10*T^62 - 73/1024*X^8*T^64 + 21/1024*X^6*T^66
    - 9/2048*X^4*T^68 + 1/2048*X^2*T^70 - 1/2048*X*Y*T^70
X^2*T^10, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^2 + x + 1)*y =
    -x^10 - 2*x^9 - 6*x^8 + 27*x^7 + 31*x^6 - 113*x^5 - 19*x^4 + 141*x^3 -
    38*x^2 - 26*x - 1 over Rational Field, 4, -1, Mapping from: Crv: top_curve
to Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^2 + x + 1)*y = -x^10 -
    2*x^9 - 6*x^8 + 27*x^7 + 31*x^6 - 113*x^5 - 19*x^4 + 141*x^3 - 38*x^2 - 26*x
    - 1 over Rational Field
with equations :
7/12*X^2*T^8 + 1/12*T^10
-42437/497664*X^10*T^40 - 8539/497664*X^8*T^42 - 2569/248832*X^6*T^44 -
    91/248832*X^4*T^46 - 25/497664*X^2*T^48 + 1/55296*Y*T^49 + 1/497664*T^50
5/12*X^2*T^8 - 1/12*T^10, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>
<[ 1, 159 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 194 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3 + x^2)*y =
    -10*x^12 + 78*x^11 - 248*x^10 + 560*x^9 - 1135*x^8 + 1726*x^7 - 2367*x^6 +
    2432*x^5 - 2188*x^4 + 1426*x^3 - 794*x^2 + 272*x - 76 over Rational Field,
5, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^5
    + x^4 + x^3 + x^2)*y = -10*x^12 + 78*x^11 - 248*x^10 + 560*x^9 - 1135*x^8 +
    1726*x^7 - 2367*x^6 + 2432*x^5 - 2188*x^4 + 1426*x^3 - 794*x^2 + 272*x - 76
over Rational Field
with equations :
-X*T^9
-1/32*X^10*T^50 - 3/16*X^9*T^51 - 3/8*X^8*T^52 - 1/4*X^7*T^53 + 11/32*X^6*T^54 +
    1/4*X^5*T^55 - 3/8*X^4*T^56 + 3/16*X^3*T^57 + 1/32*X^2*Y*T^57 -
    1/32*X^2*T^58 + 1/32*Y*T^59
-1/2*X^2*T^8 - 1/2*X*T^9 + 1/2*T^10, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        $.2,
        $.1
    ]
]>
<[ 1, 97 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^2)*y = -x^10 - 3*x^9 -
    7*x^8 - 19*x^7 - 29*x^6 - 43*x^5 - 61*x^4 - 47*x^3 - 55*x^2 - 24*x - 16 over
Rational Field, 4, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve
defined by y^2 + (x^4 + x^2)*y = -x^10 - 3*x^9 - 7*x^8 - 19*x^7 - 29*x^6 -
    43*x^5 - 61*x^4 - 47*x^3 - 55*x^2 - 24*x - 16 over Rational Field
with equations :
-1/4*X^2*T^8 - 3/4*X*T^9 + 1/4*T^10
1/1024*X^10*T^40 + 7/1024*X^9*T^41 + 13/1024*X^8*T^42 - 3/512*X^7*T^43 -
    47/1024*X^6*T^44 - 47/1024*X^5*T^45 + 47/1024*X^4*T^46 - 3/512*X^3*T^47 -
    13/1024*X^2*T^48 + 7/1024*X*T^49 + 1/256*Y*T^49 - 1/1024*T^50
-1/4*X^2*T^8 + 1/4*X*T^9 + 1/4*T^10, [
    [
        -$.3,
        -$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^2)*y = -x^10 + 3*x^9 -
    8*x^8 + 16*x^7 - 30*x^6 - 3*x^5 + 8*x^4 + 40*x^3 + 82*x^2 - 64*x - 76 over
Rational Field, 4, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve
defined by y^2 + (x^4 + x^2)*y = -x^10 + 3*x^9 - 8*x^8 + 16*x^7 - 30*x^6 - 3*x^5
    + 8*x^4 + 40*x^3 + 82*x^2 - 64*x - 76 over Rational Field
with equations :
-1/4*X^2*T^8 + 1/4*T^10
-5/16384*X^10*T^40 - 3/16384*X^8*T^42 + 7/8192*X^6*T^44 - 19/8192*X^4*T^46 +
    71/16384*X^2*T^48 + 1/1024*Y*T^49 - 39/16384*T^50
1/8*X^2*T^8 + 3/8*T^10, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>
<[ 1, 103 ], Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3 + x^2)*y =
    -2*x^11 + 3*x^10 + 10*x^9 + 82*x^8 + 54*x^7 - 184*x^6 - 1662*x^5 - 4971*x^4
    - 7210*x^3 - 4556*x^2 - 1024*x over Rational Field, 5, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3 + x^2)*y
= -2*x^11 + 3*x^10 + 10*x^9 + 82*x^8 + 54*x^7 - 184*x^6 - 1662*x^5 - 4971*x^4 -
    7210*x^3 - 4556*x^2 - 1024*x over Rational Field
with equations :
X^2*T^8
-1/2*X^10*T^50 - 1/2*X^8*T^52 - 1/2*X^6*T^54 - 1/2*X^4*T^56 - 1/2*X*Y*T^58
T^10, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 206 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ -1/2, -1, -1/2, -1/2, 0, 1/2, -1/2, 1, -1/2
    ]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, 1, 0, -1, 0, 1, 0, 0 ]) >
quotient genus = 1
quotient genus >= 2
quotient genus >= 2
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ -1/2, 1, -1/2, 1/2, 0, -1/2, -1/2, -1, -1/2
    ]) >
quotient genus = 1
quotient genus >= 2
making ShimDB object
<[ 1, 33 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
19*x[1]^2 + 982/5*x[1]*x[2] + 18661/25*x[2]^2 + 154218/125*x[2]*x[3] +
    468219/625*x[3]^2 + x[4]^2, 1, <0, "C_2^2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
19*x[1]^2 + 982/5*x[1]*x[2] + 18661/25*x[2]^2 + 154218/125*x[2]*x[3] +
    468219/625*x[3]^2 + x[4]^2
with equations :
X^4 - 4/5*X^3*T + 74/25*X^2*T^2 - 28/25*X*T^3 + 49/25*T^4
X^3*T - 7/5*X^2*T^2 + 9/5*X*T^3 - 7/5*T^4
X^2*T^2 - 2*X*T^3 + T^4
-Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        $.1 + $.3,
        4*$.2,
        $.1 - $.3
    ]
]>
<[ 1, 22 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
19*x[1]^2 - 166*x[1]*x[2] + 515*x[2]^2 - 664*x[2]*x[3] + 304*x[3]^2 + x[4]^2, 1,
<0, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
19*x[1]^2 - 166*x[1]*x[2] + 515*x[2]^2 - 664*x[2]*x[3] + 304*x[3]^2 + x[4]^2
with equations :
X^4 - 2*X^2*T^2 + T^4
-X^3*T + X*T^3
X^2*T^2
Y*T^3, [
    [
        -$.3,
        $.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 11 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -5*x^6 + 89*x^5 -
    570*x^4 + 1334*x^3 - 570*x^2 + 89*x - 5 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y =
    -5*x^6 + 89*x^5 - 570*x^4 + 1334*x^3 - 570*x^2 + 89*x - 5 over Rational
Field
with equations :
X*T^5 + T^6
1/2*X^6*T^12 - 3/2*X^5*T^13 + 3/2*X^4*T^14 - X^3*T^15 - 1/2*X^2*Y*T^15 -
    3/2*X^2*T^16 - X*Y*T^16 - 3/2*X*T^17 + 1/2*Y*T^17 - 1/2*T^18
-X^2*T^4 + X*T^5, [
    [
        -$.1 + $.3,
        -4*$.2,
        $.1 + $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^3 + x^2)*y = -5*x^6 + 15*x^5
    - 18*x^4 - 50*x^3 + 35*x^2 + 36*x - 24 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x^2)*y =
    -5*x^6 + 15*x^5 - 18*x^4 - 50*x^3 + 35*x^2 + 36*x - 24 over Rational Field
with equations :
X^2*T^4 + 2*X*T^5 - T^6
-1/2*X^6*T^12 - 7/2*X^5*T^13 - 13/2*X^4*T^14 + X^3*T^15 - 1/2*X^2*Y*T^15 +
    13/2*X^2*T^16 - 7/2*X*T^17 - 1/2*Y*T^17 + 1/2*T^18
X*T^5, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        -$.2,
        $.1
    ]
]>
<[ 1, 66 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 6 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
19*x[1]^2 + 166*x[1]*x[2] + 197*x[2]^2 - 726*x[2]*x[3] + 363*x[3]^2 + x[4]^2, 1,
<0, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
19*x[1]^2 + 166*x[1]*x[2] + 197*x[2]^2 - 726*x[2]*x[3] + 363*x[3]^2 + x[4]^2
with equations :
X^4 + 2*X^2*T^2 + T^4
X^3*T + X^2*T^2 + X*T^3 + T^4
X^2*T^2 + 2*X*T^3 + T^4
-Y*T^3, [
    [
        -$.1 + $.3,
        4*$.2,
        $.1 + $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = -6*x^6 -
    18*x^5 + 9*x^4 + 48*x^3 - 8*x^2 - 35*x - 5 over Rational Field, 2, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x +
    1)*y = -6*x^6 - 18*x^5 + 9*x^4 + 48*x^3 - 8*x^2 - 35*x - 5 over Rational
Field
with equations :
X*T^5 - T^6
1/2*X^6*T^12 + 5/2*X^5*T^13 + 7/2*X^4*T^14 - X^3*T^15 - 1/2*X^2*Y*T^15 -
    7/2*X^2*T^16 + X*Y*T^16 + 5/2*X*T^17 + 1/2*Y*T^17 - 1/2*T^18
-X^2*T^4 - 2*X*T^5 + T^6, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        $.1 + $.3,
        -4*$.2,
        $.1 - $.3
    ]
]>

computing GYData
making data-quotient list
non-hyperelliptic case
quotient genus >= 2
quotient genus >= 2
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [1, -1, -1]) >
quotient genus = 1
quotient genus >= 2
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, -1, 1]) >
quotient genus = 1
making ShimDB object
<[ 1, 34 ], Conic over Rational Field defined by
3*$.1^2 + 48*$.2^2 + $.3^2, 0, 0, 0, 0>
<[ 1, 17 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -51*x^6 + 153*x^5
    - 826*x^4 + 1396*x^3 - 3643*x^2 + 2970*x - 4386 over Rational Field, 2, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y
= -51*x^6 + 153*x^5 - 826*x^4 + 1396*x^3 - 3643*x^2 + 2970*x - 4386 over
Rational Field
with equations :
1/2*Z1*T1 + 1/2*T1^2
9/8*X1*Y1*T1^4 - 1/8*Z1^2*T1^4 - 1/2*Z1*T1^5 - 3/8*T1^6
T1^2, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        -Y1,
        Z1,
        T1
    ]
]>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -5*x^6 + 3*x^5 -
    44*x^4 - 53*x^3 - 44*x^2 + 3*x - 5 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -5*x^6 +
    3*x^5 - 44*x^4 - 53*x^3 - 44*x^2 + 3*x - 5 over Rational Field
with equations :
-1/6*Z1^2*T1^3 - 1/2*X1*T1^4 - 8/3*T1^5
1/24*X1*Y1*Z1^3*T1^10 + 1/24*X1*Z1^4*T1^10 + 2/3*X1*Y1*Z1*T1^12 +
    31/24*X1*Z1^2*T1^12 + 10*X1*T1^14
1/6*Z1^2*T1^3 - 1/2*X1*T1^4 + 8/3*T1^5, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        -Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 102 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-81/289*x[1]^2 + 10/289*x[2]^2 - 1/153*x[3]^2 + x[4]^2, 1, <1, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-81/289*x[1]^2 + 10/289*x[2]^2 - 1/153*x[3]^2 + x[4]^2
with equations :
T1^2
3*X1*T1
-3*Z1^2 - 48*T1^2
3/17*Y1*T1, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 = -9*x^6 - 27*x^5 - 94*x^4 -
    143*x^3 - 446*x^2 - 379*x - 321 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 = -9*x^6 - 27*x^5 - 94*x^4
    - 143*x^3 - 446*x^2 - 379*x - 321 over Rational Field
with equations :
1/2*X1*Z1*T1^2 + 1/6*Z1^2*T1^2 + 8/3*T1^4
-8/3*X1*Y1*Z1^2*T1^8 - 128/3*X1*Y1*T1^10
-1/3*Z1^2*T1^2 - 16/3*T1^4, [
    [
        -X1,
        -Y1,
        -Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 51 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-81/289*x[1]^2 - 214/289*x[2]^2 - 17/9*x[3]^2 + x[4]^2, 1, <0, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-81/289*x[1]^2 - 214/289*x[2]^2 - 17/9*x[3]^2 + x[4]^2
with equations :
Z1^2
3*X1*Z1
-3*Z1^2 - 48*T1^2
-48/17*Y1*T1, [
    [
        -X1,
        Y1,
        -Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 2 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-1/153*x[1]^2 - 574/2601*x[2]^2 - 17/9*x[3]^2 + x[4]^2, 1, <0, "C_2^2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-1/153*x[1]^2 - 574/2601*x[2]^2 - 17/9*x[3]^2 + x[4]^2
with equations :
Z1^2
-Z1*T1
T1^2
1/17*Y1*T1, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        Y1,
        Z1,
        T1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
quotient genus >= 2
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, 1, 0, -1, 0, 1, 0, 0 ]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, -1, 0, -1, 0, -1, 0, 0 ]) >
quotient genus = 1
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 19 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
76*x[1]^2 + 840*x[1]*x[2] + 2500*x[2]^2 + 840*x[2]*x[3] + 76*x[3]^2 + x[4]^2, 1,
<0, "C_2^2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
76*x[1]^2 + 840*x[1]*x[2] + 2500*x[2]^2 + 840*x[2]*x[3] + 76*x[3]^2 + x[4]^2
with equations :
X^4
-X^2*T^2
T^4
2*Y*T^3, [
    [
        $.1,
        $.2,
        -$.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 38 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = -19*x^6 +
    57*x^5 + 19*x^4 - 134*x^3 - 22*x^2 + 97*x + 38 over Rational Field, 2, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x +
    1)*y = -19*x^6 + 57*x^5 + 19*x^4 - 134*x^3 - 22*x^2 + 97*x + 38 over
Rational Field
with equations :
1/2*X^2*T^3 + 1/2*X*T^4 + 1/2*T^5
-1/8*X^5*T^10 - 1/2*X^4*T^11 - 9/8*X^3*T^12 - 1/8*X^2*Y*T^12 - 1/2*X^2*T^13 -
    1/8*X*T^14 + 1/8*Y*T^14
X*T^4, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        $.3,
        -$.2,
        $.1
    ]
]>
<[ 1, 57 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
19*x[1]^2 - 134*x[2]^2 + 243*x[3]^2 + x[4]^2, 1, <0, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
19*x[1]^2 - 134*x[2]^2 + 243*x[3]^2 + x[4]^2
with equations :
X^4 - 2*X^2*T^2 + T^4
-X^3*T + X*T^3
X^2*T^2
Y*T^3, [
    [
        -$.3,
        $.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 3 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
19*x[1]^2 - 286*x[2]^2 + 1083*x[3]^2 + x[4]^2, 1, <0, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
19*x[1]^2 - 286*x[2]^2 + 1083*x[3]^2 + x[4]^2
with equations :
X^4 + 2*X^2*T^2 + T^4
-X^3*T - X*T^3
X^2*T^2
Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        $.3,
        $.2,
        $.1
    ]
]>
<[ 1, 114 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 = 19*x^5 + 210*x^4 + 625*x^3 +
    210*x^2 + 19*x over Rational Field, 2, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 = 19*x^5 + 210*x^4 + 625*x^3 + 210*x^2 + 19*x
over Rational Field
with equations :
T^2
-X*Y*T^4
-X^2, [
    [
        $.1,
        -$.2,
        -$.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -19*x^6 - 57*x^5 -
    57*x^4 - 19*x^3 + 22*x^2 + 22*x - 10 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y =
    -19*x^6 - 57*x^5 - 57*x^4 - 19*x^3 + 22*x^2 + 22*x - 10 over Rational Field
with equations :
1/2*X^2*T^3 - 1/2*X*T^4 - 1/2*T^5
-1/8*X^5*T^10 + 3/8*X^3*T^12 - 1/8*X^2*Y*T^12 - 1/8*X*T^14 - 1/8*Y*T^14
X*T^4, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        -$.2,
        $.1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 174 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 58 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -x^6 + 6*x^5 -
    16*x^4 + 18*x^3 - 16*x^2 + 6*x - 1 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -x^6 +
    6*x^5 - 16*x^4 + 18*x^3 - 16*x^2 + 6*x - 1 over Rational Field
with equations :
-1/6*X^2*T^3 - 1/2*X*T^4 + 1/3*T^5
1/24*X^5*T^10 - 1/24*X^3*T^12 + 1/6*X*T^14 - 1/216*Y*T^14
1/6*X^2*T^3 - 1/2*X*T^4 - 1/3*T^5, [
    [
        -2*$.3,
        -8*$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 87 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -12*x^8 + 24*x^7
    + 34*x^6 - 72*x^5 - 17*x^4 + 48*x^3 - 24*x^2 + 5*x + 13 over Rational Field,
3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2
    + x)*y = -12*x^8 + 24*x^7 + 34*x^6 - 72*x^5 - 17*x^4 + 48*x^3 - 24*x^2 + 5*x
    + 13 over Rational Field
with equations :
1/3*X^2*T^6 + 1/3*T^8
-1/81*X^8*T^24 + 7/162*X^6*T^26 - 1/54*X^4*T^28 - 4/81*X^2*T^30 + 1/54*X*Y*T^30
    + 2/81*T^32
1/3*X^2*T^6 - 2/3*T^8, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 29 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -16*x^8 + 523*x^6
    - 6131*x^4 + 29845*x^2 - 48778 over Rational Field, 3, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -16*x^8 +
    523*x^6 - 6131*x^4 + 29845*x^2 - 48778 over Rational Field
with equations :
X^2*T^5 + 2*T^7
1/2*X^7*T^21 + 7/2*X^5*T^23 + 7*X^3*T^25 - 1/2*X^2*Y*T^25 + 4*X*T^27 + Y*T^27
-X*T^6, [
    [
        -2*$.3,
        -8*$.2,
        -$.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -6*x^8 + 21*x^6 +
    41*x^4 - 117*x^2 - 144 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -6*x^8 + 21*x^6
    + 41*x^4 - 117*x^2 - 144 over Rational Field
with equations :
-X*T^6
-1/54*X^7*T^21 - 1/18*X^5*T^23 + 1/9*X^3*T^25 + 1/54*X^2*Y*T^25 + 4/27*X*T^27 +
    1/27*Y*T^27
-1/3*X^2*T^5 + 2/3*T^7, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -2*$.3,
        8*$.2,
        $.1
    ]
]>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = -64*x^6 -
    192*x^5 + 155*x^4 + 630*x^3 - 210*x^2 - 557*x + 219 over Rational Field, 2,
-1, Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 +
    x + 1)*y = -64*x^6 - 192*x^5 + 155*x^4 + 630*x^3 - 210*x^2 - 557*x + 219
over Rational Field
with equations :
1/2*X^2*T^3 - 1/2*X*T^4 + T^5
-1/8*X^5*T^10 - 7/8*X^3*T^12 - 1/2*X*T^14 - 1/8*Y*T^14
X*T^4, [
    [
        -2*$.3,
        8*$.2,
        -$.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 = -24*x^6 - 36*x^5 + 74*x^4 +
    89*x^3 - 41*x^2 - 32*x - 52 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 = -24*x^6 - 36*x^5 + 74*x^4 +
    89*x^3 - 41*x^2 - 32*x - 52 over Rational Field
with equations :
1/3*X^2 + 1/3*T^2
-1/27*Y*T^5
-1/3*X^2 + 2/3*T^2, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
MatrixGroup<5, RationalField() |
    ScalarMatrix(RationalField(), 5, -1) >
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 31 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^2 + 1)*y = -11*x^8 -
    69*x^7 - 134*x^6 - 96*x^5 - 103*x^4 - 96*x^3 - 134*x^2 - 69*x - 11 over
Rational Field, 3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve
defined by y^2 + (x^4 + x^2 + 1)*y = -11*x^8 - 69*x^7 - 134*x^6 - 96*x^5 -
    103*x^4 - 96*x^3 - 134*x^2 - 69*x - 11 over Rational Field
with equations :
1/4*X^2*T^6 - 1/2*X*T^7 - 3/4*T^8
-3/512*X^8*T^24 - 1/128*X^6*T^26 + 15/256*X^4*T^28 + 1/512*X^2*Y*T^29 -
    9/128*X^2*T^30 + 3/512*Y*T^31 - 243/512*T^32
-1/4*X^2*T^6 - 1/2*X*T^7 + 3/4*T^8, [
    [
        -3*$.3,
        27*$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 93 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 8*x^6 + 24*x^5 +
    9*x^4 - 22*x^3 - 8*x^2 + 7*x - 1 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 8*x^6 +
    24*x^5 + 9*x^4 - 22*x^3 - 8*x^2 + 7*x - 1 over Rational Field
with equations :
-1/16*X^2*T^4 - 1/2*X*T^5 - 3/16*T^6
1/4096*X^6*T^12 - 55/4096*X^4*T^14 - 165/4096*X^2*T^16 - 1/4096*Y*T^17 +
    27/4096*T^18
1/8*X^2*T^4 + 3/8*T^6, [
    [
        3*$.3,
        27*$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 186 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -x^6 - 3*x^5 + x^4
    - 29*x^3 - 99*x^2 + 118*x - 31 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -x^6 -
    3*x^5 + x^4 - 29*x^3 - 99*x^2 + 118*x - 31 over Rational Field
with equations :
3/16*X^2*T^4 + 1/16*T^6
-13/4096*X^6*T^12 - 21/4096*X^4*T^14 + 33/4096*X^2*T^16 - 1/4096*Y*T^17 -
    63/4096*T^18
-1/16*X^2*T^4 + 5/16*T^6, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 = -43*x^6 - 233*x^5 - 258*x^4 +
    107*x^3 - 258*x^2 - 233*x - 43 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 = -43*x^6 - 233*x^5 -
    258*x^4 + 107*x^3 - 258*x^2 - 233*x - 43 over Rational Field
with equations :
1/4*X^2 + 1/2*X*T - 3/4*T^2
-1/64*Y*T^5
-1/4*X^2 + 1/2*X*T + 3/4*T^2, [
    [
        -3*$.3,
        -27*$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -6*x^8 + 94*x^6 -
    523*x^4 + 1198*x^2 - 972 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -6*x^8 + 94*x^6
    - 523*x^4 + 1198*x^2 - 972 over Rational Field
with equations :
-X*T^6
-1/1024*X^7*T^21 - 73/1024*X^5*T^23 - 219/1024*X^3*T^25 - 1/2048*X^2*Y*T^25 -
    27/1024*X*T^27 + 3/2048*Y*T^27
-1/8*X^2*T^5 - 3/8*T^7, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        3*$.3,
        -27*$.2,
        $.1
    ]
]>
<[ 1, 62 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -60*x^8 + 36*x^7
    + 155*x^6 - 473*x^5 - 191*x^4 + 847*x^3 - 88*x^2 - 432*x + 162 over Rational
Field, 3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2
+ (x^2 + x)*y = -60*x^8 + 36*x^7 + 155*x^6 - 473*x^5 - 191*x^4 + 847*x^3 -
    88*x^2 - 432*x + 162 over Rational Field
with equations :
-1/8*X^2*T^4 - 3/8*T^6
-1/1024*X^6*T^18 + 7/1024*X^4*T^20 + 5/1024*X^2*T^22 + 1/1024*X*Y*T^22 -
    75/1024*T^24
1/8*X^2*T^4 - 5/8*T^6, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        -$.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 37 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -17*x^6 + 22*x^5
    - 60*x^4 + 45*x^3 - 60*x^2 + 22*x - 17 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y =
    -17*x^6 + 22*x^5 - 60*x^4 + 45*x^3 - 60*x^2 + 22*x - 17 over Rational Field
with equations :
1/6*X^2*T^4 + 1/4*X*T^5 - 1/6*T^6
-1/216*X^6*T^12 - 5/288*X^4*T^14 + 5/288*X^2*T^16 - 1/1728*Y*T^17 + 1/216*T^18
1/6*X^2*T^4 - 1/4*X*T^5 - 1/6*T^6, [
    [
        $.3,
        -$.2,
        -$.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 74 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -16*x^8 + 351*x^6
    - 1721*x^4 + 3153*x^2 - 148 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -16*x^8 +
    351*x^6 - 1721*x^4 + 3153*x^2 - 148 over Rational Field
with equations :
X^2*T^5 + T^7
1/4*X^7*T^21 + 13/16*X^5*T^23 + 13/16*X^3*T^25 + 1/16*X^2*Y*T^25 + 1/4*X*T^27 -
    1/16*Y*T^27
-1/2*X*T^6, [
    [
        $.3,
        -$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 111 ], Hyperelliptic Curve defined by y^2 + (x^2)*y = 20*x^8 + 48*x^7 +
    30*x^6 - 12*x^5 - 89*x^4 - 12*x^3 + 30*x^2 + 48*x + 20 over Rational Field,
3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 +
(x^2)*y = 20*x^8 + 48*x^7 + 30*x^6 - 12*x^5 - 89*x^4 - 12*x^3 + 30*x^2 + 48*x +
    20 over Rational Field
with equations :
-2/3*X^2*T^6 - 1/3*T^8
-2/81*X^8*T^24 - 10/81*X^6*T^26 - 11/54*X^4*T^28 - 10/81*X^2*T^30 +
    1/54*X*Y*T^30 - 2/81*T^32
1/3*X^2*T^6 + 2/3*T^8, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 222 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -7*x^6 - 27*x^5 +
    104*x^3 - 27*x - 7 over Rational Field, 2, -1, Mapping from: Crv: top_curve
to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -7*x^6 - 27*x^5 + 104*x^3
    - 27*x - 7 over Rational Field
with equations :
-1/2*X^2*T^3 + 1/4*X*T^4 - 1/2*T^5
-3/16*X^5*T^10 - 25/64*X^3*T^12 - 3/16*X*T^14 - 1/64*Y*T^14
1/2*X^2*T^3 + 1/4*X*T^4 + 1/2*T^5, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        $.3,
        $.2,
        $.1
    ]
]>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -144*x^8 - 929*x^6
    - 2245*x^4 - 2411*x^2 - 972 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -144*x^8 -
    929*x^6 - 2245*x^4 - 2411*x^2 - 972 over Rational Field
with equations :
1/3*X^2*T^5 - 1/3*T^7
1/108*X^7*T^21 - 1/144*X^5*T^23 + 1/144*X^3*T^25 + 1/432*X^2*Y*T^25 -
    1/108*X*T^27 + 1/432*Y*T^27
-1/2*X*T^6, [
    [
        $.3,
        $.2,
        -$.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 = -40*x^6 + 4*x^5 - 30*x^4 +
    95*x^3 - 30*x^2 + 4*x - 40 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 = -40*x^6 + 4*x^5 - 30*x^4 +
    95*x^3 - 30*x^2 + 4*x - 40 over Rational Field
with equations :
-1/3*X^2 - 2/3*T^2
-1/27*Y*T^5
2/3*X^2 + 1/3*T^2, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 5 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^8 + 31*x^6 -
    117*x^4 - 43*x^2 - 10 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^8 + 31*x^6
    - 117*x^4 - 43*x^2 - 10 over Rational Field
with equations :
X^2*T^5 + 2*T^7
1/2*X^7*T^21 + 7/2*X^5*T^23 + 7*X^3*T^25 - 1/2*X^2*Y*T^25 + 4*X*T^27 + Y*T^27
-X*T^6, [
    [
        2*$.3,
        -8*$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 55 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = 2*x^7 + 5*x^6 -
    18*x^5 - 30*x^4 + 67*x^3 + 21*x^2 - 41*x + 13 over Rational Field, 3, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y
= 2*x^7 + 5*x^6 - 18*x^5 - 30*x^4 + 67*x^3 + 21*x^2 - 41*x + 13 over Rational
Field
with equations :
X^2*T^4 + T^6
1/2*X^6*T^18 + 3/2*X^4*T^20 + 2*X^2*T^22 + 1/2*X*Y*T^22 + T^24
-T^6, [
    [
        -2*$.1,
        -64*$.2,
        2*$.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 110 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 22 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = x^6 - 2*x^4 -
    7*x^3 - 2*x^2 + 1 over Rational Field, 2, -1, Mapping from: Crv: top_curve
to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = x^6 - 2*x^4 - 7*x^3 -
    2*x^2 + 1 over Rational Field
with equations :
-1/2*X^2*T^4 + 1/2*X*T^5 - T^6
1/8*X^6*T^12 + 9/8*X^4*T^14 + 9/4*X^2*T^16 - 1/8*Y*T^17 + T^18
-1/2*X^2*T^4 - 1/2*X*T^5 - T^6, [
    [
        2*$.3,
        8*$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 11 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^8 - 49*x^6 -
    397*x^4 - 1079*x^2 - 22 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^8 - 49*x^6
    - 397*x^4 - 1079*x^2 - 22 over Rational Field
with equations :
X^2*T^5 - 2*T^7
1/2*X^7*T^21 - 5/2*X^5*T^23 + 5*X^3*T^25 + 1/2*X^2*Y*T^25 - 4*X*T^27 + Y*T^27
-X*T^6, [
    [
        -2*$.3,
        8*$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 10 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -11*x^6 + 13*x^5
    + 6*x^4 - 25*x^3 + 6*x^2 + 13*x - 11 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y =
    -11*x^6 + 13*x^5 + 6*x^4 - 25*x^3 + 6*x^2 + 13*x - 11 over Rational Field
with equations :
-1/2*X^2*T^4 + 1/2*X*T^5 + T^6
1/8*X^6*T^12 - 3/8*X^4*T^14 + 3/4*X^2*T^16 - 1/8*Y*T^17 - T^18
-1/2*X^2*T^4 - 1/2*X*T^5 + T^6, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -2*$.3,
        -8*$.2,
        $.1
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 = -8*x^6 + 61*x^5 - 100*x^4 -
    83*x^3 + 58*x^2 + 60*x - 40 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 = -8*x^6 + 61*x^5 - 100*x^4 -
    83*x^3 + 58*x^2 + 60*x - 40 over Rational Field
with equations :
X^2 + 2*T^2
-Y*T^5
T^2, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -2*$.1,
        64*$.2,
        2*$.3
    ]
]>

computing GYData
making data-quotient list
non-hyperelliptic case
quotient genus >= 2
quotient genus >= 2
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [1, -1, -1]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, -1, 1]) >
quotient genus = 1
quotient genus >= 2
making ShimDB object
<[ 1, 26 ], Hyperelliptic Curve defined by y^2 = -53*x^6 - 50*x^5 - 172*x^4 -
    100*x^3 - 172*x^2 - 50*x - 53 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 = -53*x^6 - 50*x^5 - 172*x^4 -
    100*x^3 - 172*x^2 - 50*x - 53 over Rational Field
with equations :
-1/10*Z1*T1 - 1/2*T1^2
1/50*X1*Y1*T1^4
1/10*Z1*T1 - 1/2*T1^2, [
    [
        -X1,
        -Y1,
        Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 5 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = -13*x^6 -
    39*x^5 - 87*x^4 - 109*x^3 - 106*x^2 - 58*x - 22 over Rational Field, 2, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x +
    1)*y = -13*x^6 - 39*x^5 - 87*x^4 - 109*x^3 - 106*x^2 - 58*x - 22 over
Rational Field
with equations :
1/2*X1*Z1*T1^4 + 1/4*Z1^2*T1^4 + 25/4*T1^6
1/64*Z1^6*T1^12 - 25/16*X1*Y1*Z1^2*T1^14 + 125/64*Z1^4*T1^14 -
    625/16*X1*Y1*T1^16 + 4375/64*Z1^2*T1^16 + 46875/64*T1^18
-1/2*Z1^2*T1^4 - 25/2*T1^6, [
    [
        -X1,
        -Y1,
        -Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 130 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-208*x[1]^2 + 296/25*x[2]^2 - 1/5*x[3]^2 + x[4]^2, 1, <1, "C_6">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-208*x[1]^2 + 296/25*x[2]^2 - 1/5*x[3]^2 + x[4]^2
with equations :
T1^2
2*X1*T1
-2*Z1^2 - 50*T1^2
4/5*Y1*T1, [
    [
        X1,
        Y1,
        -Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 13 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-208*x[1]^2 - 504*x[2]^2 - 325*x[3]^2 + x[4]^2, 1, <0, "C_2^2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-208*x[1]^2 - 504*x[2]^2 - 325*x[3]^2 + x[4]^2
with equations :
Z1^2
2*X1*Z1
-2*Z1^2 - 50*T1^2
-20*Y1*T1, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 65 ], Conic over Rational Field defined by
2*$.1^2 + 50*$.2^2 + $.3^2, 0, 0, 0, 0>
<[ 1, 10 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-1/5*x[1]^2 - 398/25*x[2]^2 - 325*x[3]^2 + x[4]^2, 1, <0, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-1/5*x[1]^2 - 398/25*x[2]^2 - 325*x[3]^2 + x[4]^2
with equations :
Z1^2
-Z1*T1
T1^2
2/5*Y1*T1, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -3*x^6 + 23*x^5 -
    63*x^4 + 72*x^3 - 63*x^2 + 23*x - 3 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y =
    -3*x^6 + 23*x^5 - 63*x^4 + 72*x^3 - 63*x^2 + 23*x - 3 over Rational Field
with equations :
1/20*Z1^2*T1^3 + 1/2*X1*T1^4 + 5/4*T1^5
1/400*X1*Y1*Z1^3*T1^10 + 1/800*X1*Z1^4*T1^10 + 1/16*X1*Y1*Z1*T1^12 +
    1/8*X1*Z1^2*T1^12 + 75/32*X1*T1^14
-1/20*Z1^2*T1^3 + 1/2*X1*T1^4 - 5/4*T1^5, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        -Y1,
        -Z1,
        T1
    ]
]>

computing GYData
making data-quotient list
non-hyperelliptic case
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 5 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^8 + 21*x^6 -
    127*x^4 + 135*x^2 - 40 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^8 + 21*x^6
    - 127*x^4 + 135*x^2 - 40 over Rational Field
with equations :
-X1*T1^6 - 1/5*T1^7
1/2000*X1*Z1^6*T1^21 - 1/400*Y1*Z1^5*T1^22 + 1/2500*Z1^6*T1^22 -
    1/100*X1*Y1*Z1^3*T1^23 + 293/5000*X1*Z1^4*T1^23 - 163/1000*Y1*Z1^3*T1^24 +
    581/12500*Z1^4*T1^24 - 161/500*X1*Y1*Z1*T1^25 + 111321/50000*X1*Z1^2*T1^25 -
    26561/10000*Y1*Z1*T1^26 + 5461/3125*Z1^2*T1^26 + 345293/12500*X1*T1^27 +
    66976/3125*T1^28
1/10*Z1^2*T1^5 + 1/10*X1*T1^6 + 16/5*T1^7, [
    [
        X1,
        -Y1,
        -Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 19 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -8*x^8 - 185*x^6
    - 1425*x^4 - 3673*x^2 - 38 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -8*x^8 - 185*x^6
    - 1425*x^4 - 3673*x^2 - 38 over Rational Field
with equations :
-1/2*Z1*T1^2
-1/16*Z1^3*T1^9 - 25/16*X1*Y1*T1^10 - 1/4*Z1*T1^11
-T1^3, [
    [
        -X1,
        -Y1,
        Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 38 ], Conic over Rational Field defined by
$.1^2 - 160*$.2^2 - 5*$.3^2, 0, 0, 0, 0>
<[ 1, 95 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^2 + 1)*y = x^7 + 5*x^6
    + 13*x^5 + 55*x^4 + 91*x^3 + 7*x^2 - 36*x - 12 over Rational Field, 3, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^4 + x^2
    + 1)*y = x^7 + 5*x^6 + 13*x^5 + 55*x^4 + 91*x^3 + 7*x^2 - 36*x - 12 over
Rational Field
with equations :
-X1*Z1*T1^6 + 8*T1^8
-1/5*X1*Z1^7*T1^24 - 3/25*Z1^8*T1^24 - 56/5*X1*Z1^5*T1^26 - 272/25*Z1^6*T1^26 -
    60*X1*Y1*Z1^3*T1^27 - 28*Y1*Z1^4*T1^27 - 1168/5*X1*Z1^3*T1^28 -
    10192/25*Z1^4*T1^28 - 1600*X1*Y1*Z1*T1^29 - 1280*Y1*Z1^2*T1^29 -
    1536*X1*Z1*T1^30 - 35584/5*Z1^2*T1^30 - 12800*Y1*T1^31 - 43008*T1^32
-1/2*X1*Z1*T1^6 - 1/2*Z1^2*T1^6 - 16*T1^8, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 190 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = x^6 - 3*x^5
    + x^4 + 2*x^3 - 3*x over Rational Field, 2, -1, Mapping from: Crv: top_curve
to Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = x^6 - 3*x^5 + x^4 +
    2*x^3 - 3*x over Rational Field
with equations :
1/20*Z1^2*T1^4 - 1/2*X1*T1^5 + 8/5*T1^6
-7/8000*Z1^6*T1^12 + 1/200*X1*Z1^4*T1^13 + 1/160*X1*Y1*Z1^2*T1^14 -
    173/2000*Z1^4*T1^14 + 8/25*X1*Z1^2*T1^15 + 1/5*X1*Y1*T1^16 -
    356/125*Z1^2*T1^16 + 128/25*X1*T1^17 - 3904/125*T1^18
1/10*Z1^2*T1^4 + 16/5*T1^6, [
    [
        X1,
        Y1,
        -Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 10 ], Hyperelliptic Curve defined by y^2 = -2*x^6 + 6*x^5 - 40*x^4 +
    70*x^3 - 416*x^2 + 382*x - 94 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 = -2*x^6 + 6*x^5 - 40*x^4 +
    70*x^3 - 416*x^2 + 382*x - 94 over Rational Field
with equations :
-1/2*X1*Z1*T1^2 + 1/10*Z1^2*T1^2 + 16/5*T1^4
8/5*X1*Y1*Z1^2*T1^8 + 256/5*X1*Y1*T1^10
1/5*Z1^2*T1^2 + 32/5*T1^4, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        -Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -185*x^6 - 205*x^5
    + 121*x^4 + 442*x^3 + 121*x^2 - 205*x - 185 over Rational Field, 2, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y
= -185*x^6 - 205*x^5 + 121*x^4 + 442*x^3 + 121*x^2 - 205*x - 185 over Rational
Field
with equations :
1/4*Z1*T1 + 1/2*T1^2
1/32*Z1^2*T1^4 + 25/32*Y1*T1^5 - 1/8*T1^6
-1/4*Z1*T1 + 1/2*T1^2, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        Y1,
        Z1,
        T1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 5 ], Hyperelliptic Curve defined by y^2 + (x^3 + x^2)*y = -172*x^10 +
    224*x^9 - 574*x^8 - 78*x^7 - 957*x^6 - 356*x^5 - 2928*x^4 + 1599*x^3 -
    3657*x^2 + 1588*x - 940 over Rational Field, 4, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x^2)*y = -172*x^10 +
    224*x^9 - 574*x^8 - 78*x^7 - 957*x^6 - 356*x^5 - 2928*x^4 + 1599*x^3 -
    3657*x^2 + 1588*x - 940 over Rational Field
with equations :
1/2*X^2*T^6 - 1/2*X*T^7 - 1/2*T^8
-1/16*X^8*T^32 + 5/16*X^7*T^33 - 1/4*X^6*T^34 - 7/16*X^5*T^35 + 1/4*X^4*T^36 +
    5/16*X^3*T^37 + 1/16*X^2*T^38 + 1/16*Y*T^39
-X*T^7, [
    [
        -$.3,
        -$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 23 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^2 + 1)*y = 20*x^12 +
    120*x^11 + 318*x^10 + 490*x^9 + 451*x^8 + 185*x^7 - 62*x^6 - 94*x^5 + 3*x^4
    + 60*x^3 - 29*x - 11 over Rational Field, 5, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^4 + x^2 + 1)*y = 20*x^12 +
    120*x^11 + 318*x^10 + 490*x^9 + 451*x^8 + 185*x^7 - 62*x^6 - 94*x^5 + 3*x^4
    + 60*x^3 - 29*x - 11 over Rational Field
with equations :
-1/5*X^2*T^10 + 2/5*X*T^11
-3/31250*X^12*T^60 + 6/15625*X^11*T^61 - 4/3125*X^10*T^62 + 32/15625*X^9*T^63 -
    51/15625*X^8*T^64 + 48/15625*X^7*T^65 - 52/15625*X^6*T^66 +
    24/15625*X^5*T^67 - 24/15625*X^4*T^68 + 2/15625*X^3*T^69 +
    1/31250*X^2*Y*T^69 - 1/3125*X^2*T^70 + 1/31250*X*Y*T^70 - 1/31250*Y*T^71 -
    1/31250*T^72
1/5*X^2*T^10 + 1/5*T^12, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        $.1 - 2*$.3,
        -3125*$.2,
        -2*$.1 - $.3
    ]
]>
<[ 1, 230 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 46 ], Hyperelliptic Curve defined by y^2 + (x^6 + x^5 + x^4 + x^3)*y =
    -11*x^12 + 49*x^11 - 254*x^10 + 387*x^9 - 1597*x^8 + 1007*x^7 - 15073*x^6 +
    32659*x^5 - 142651*x^4 + 231800*x^3 - 454352*x^2 + 374400*x - 300800 over
Rational Field, 5, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve
defined by y^2 + (x^6 + x^5 + x^4 + x^3)*y = -11*x^12 + 49*x^11 - 254*x^10 +
    387*x^9 - 1597*x^8 + 1007*x^7 - 15073*x^6 + 32659*x^5 - 142651*x^4 +
    231800*x^3 - 454352*x^2 + 374400*x - 300800 over Rational Field
with equations :
X^2*T^10 - X*T^11 - T^12
-1/2*X^12*T^60 + 7/2*X^11*T^61 - 15/2*X^10*T^62 + 35/2*X^8*T^64 - 17/2*X^7*T^65
    - 21*X^6*T^66 + 17/2*X^5*T^67 + 35/2*X^4*T^68 + 1/2*X^2*Y*T^69 -
    15/2*X^2*T^70 - 7/2*X*T^71 + 1/2*Y*T^71 - 1/2*T^72
-X*T^11, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        $.2,
        $.1
    ]
]>
<[ 1, 115 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^2)*y = -2*x^10 +
    21*x^8 - 117*x^6 + 361*x^4 - 552*x^2 + 320 over Rational Field, 4, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^4 +
    x^2)*y = -2*x^10 + 21*x^8 - 117*x^6 + 361*x^4 - 552*x^2 + 320 over Rational
Field
with equations :
-X^2*T^8 - T^10
-5/16*X^10*T^40 - 7/16*X^9*T^41 - 7/8*X^8*T^42 - 17/16*X^7*T^43 - 9/16*X^6*T^44
    - 5/4*X^5*T^45 + 9/16*X^4*T^46 - 17/16*X^3*T^47 + 7/8*X^2*T^48 - 7/16*X*T^49
    - 1/16*Y*T^49 + 5/16*T^50
1/2*X^2*T^8 + 1/2*X*T^9 - 1/2*T^10, [
    [
        2*$.1 + $.3,
        3125*$.2,
        $.1 - 2*$.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 10 ], Hyperelliptic Curve defined by y^2 = -43*x^10 - 271*x^9 - 704*x^8 -
    917*x^7 - 745*x^6 - 528*x^5 - 745*x^4 - 917*x^3 - 704*x^2 - 271*x - 43 over
Rational Field, 4, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve
defined by y^2 = -43*x^10 - 271*x^9 - 704*x^8 - 917*x^7 - 745*x^6 - 528*x^5 -
    745*x^4 - 917*x^3 - 704*x^2 - 271*x - 43 over Rational Field
with equations :
1/2*X*T + 1/4*T^2
-1/1024*Y*T^9
1/4*X^2 - 1/2*X*T, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        $.1 - 2*$.3,
        3125*$.2,
        -2*$.1 - $.3
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^3)*y = -80*x^12 + 652*x^10 -
    2135*x^8 + 3670*x^6 - 3690*x^4 + 2212*x^2 - 640 over Rational Field, 5, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3)*y =
    -80*x^12 + 652*x^10 - 2135*x^8 + 3670*x^6 - 3690*x^4 + 2212*x^2 - 640 over
Rational Field
with equations :
-X^2*T^10 - X*T^11 + T^12
-1/2*X^12*T^60 - 3/2*X^11*T^61 - 3/2*X^10*T^62 - 2*X^9*T^63 - 3/2*X^8*T^64 +
    3/2*X^7*T^65 + 3/2*X^5*T^67 + 3/2*X^4*T^68 - 2*X^3*T^69 - 1/2*X^2*Y*T^69 +
    3/2*X^2*T^70 + 2*X*Y*T^70 - 3/2*X*T^71 + 1/2*Y*T^71 + 1/2*T^72
-X^2*T^10 - T^12, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        2*$.1 + $.3,
        -3125*$.2,
        $.1 - 2*$.3
    ]
]>

computing GYData
making data-quotient list
non-hyperelliptic case
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [1, -1, -1]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, -1, 1]) >
quotient genus = 1
making ShimDB object
<[ 1, 21 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-81/49*x[1]^2 + 26/49*x[2]^2 + 7/81*x[3]^2 + x[4]^2, 1, <0, "C_6">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-81/49*x[1]^2 + 26/49*x[2]^2 + 7/81*x[3]^2 + x[4]^2
with equations :
Z1^2
9*X1*Z1
-9*Z1^2 - 18*T1^2
18/7*Y1*T1, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 14 ], Conic over Rational Field defined by
9*$.1^2 + 18*$.2^2 + $.3^2, 0, 0, 0, 0>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = -2*x^6 - 6*x^5
    - 21*x^4 - 32*x^3 - 34*x^2 - 19*x - 3 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y =
    -2*x^6 - 6*x^5 - 21*x^4 - 32*x^3 - 34*x^2 - 19*x - 3 over Rational Field
with equations :
1/18*Z1^2*T1^4 + 1/2*X1*T1^5 + 1/9*T1^6
1/1944*Z1^6*T1^12 - 1/72*X1*Y1*Z1^3*T1^13 + 1/648*Z1^4*T1^14 -
    1/36*X1*Y1*Z1*T1^15 - 1/486*T1^18
-1/9*Z1^2*T1^4 - 2/9*T1^6, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        -Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 7 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 7*x^6 + 21*x^5 +
    86*x^4 + 137*x^3 + 146*x^2 + 81*x + 27 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 7*x^6
    + 21*x^5 + 86*x^4 + 137*x^3 + 146*x^2 + 81*x + 27 over Rational Field
with equations :
1/2*Z1*T1 - 1/2*T1^2
27/8*X1*Y1*T1^4 - 1/8*Z1^2*T1^4 + 1/8*T1^6
T1^2, [
    [
        -X1,
        -Y1,
        Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 = -2*x^6 - 6*x^5 + x^4 + 12*x^3 +
    83*x^2 + 76*x + 115 over Rational Field, 2, -1, Mapping from: Crv: top_curve
to Hyperelliptic Curve defined by y^2 = -2*x^6 - 6*x^5 + x^4 + 12*x^3 + 83*x^2 +
    76*x + 115 over Rational Field
with equations :
1/2*X1*Z1*T1^2 + 1/18*Z1^2*T1^2 + 1/9*T1^4
1/18*X1*Y1*Z1^2*T1^8 + 1/9*X1*Y1*T1^10
-1/9*Z1^2*T1^2 - 2/9*T1^4, [
    [
        -X1,
        -Y1,
        -Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 42 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-81/49*x[1]^2 - 22/49*x[2]^2 + 1/567*x[3]^2 + x[4]^2, 1, <0, "C_6">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
-81/49*x[1]^2 - 22/49*x[2]^2 + 1/567*x[3]^2 + x[4]^2
with equations :
T1^2
9*X1*T1
-9*Z1^2 - 18*T1^2
-9/7*Y1*T1, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 2 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
1/567*x[1]^2 + 226/3969*x[2]^2 + 7/81*x[3]^2 + x[4]^2, 1, <0, "C_2^2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
1/567*x[1]^2 + 226/3969*x[2]^2 + 7/81*x[3]^2 + x[4]^2
with equations :
Z1^2
-Z1*T1
T1^2
-1/7*Y1*T1, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        Y1,
        Z1,
        T1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ -4/5, 4/5, -1/5, 2/5, 3/5, -2/5, -1/5, -4/5,
    -4/5 ]) >
quotient genus = 1
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ -1/5, -4/5, -4/5, -2/5, -3/5, 2/5, -4/5,
    4/5, -1/5 ]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, 1, 0, -1, 0, 1, 0, 0 ]) >
quotient genus = 1
making ShimDB object
<[ 1, 5 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
23*x[1]^2 + 274458/1271*x[1]*x[2] + 445870093/3230882*x[2]^2 +
    75751624885/4106451022*x[2]*x[3] - 105061922739001/41754393991696*x[3]^2 +
    x[4]^2, 1, <0, "C_6">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
23*x[1]^2 + 274458/1271*x[1]*x[2] + 445870093/3230882*x[2]^2 +
    75751624885/4106451022*x[2]*x[3] - 105061922739001/41754393991696*x[3]^2 +
    x[4]^2
with equations :
X^4 - 993/1271*X^3*T + 3812753/6461764*X^2*T^2 - 276054/1615441*X*T^3 +
    77284/1615441*T^4
X^3*T + 4091/2542*X^2*T^2 - 715/1271*X*T^3 + 556/1271*T^4
X^2*T^2 + 4*X*T^3 + 4*T^4
-Y*T^3, [
    [
        $.1 - 1/2*$.3,
        25/16*$.2,
        -1/2*$.1 - $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 70 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -3*x^6 - 16*x^5 -
    10*x^4 + 41*x^3 - 10*x^2 - 16*x - 3 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y =
    -3*x^6 - 16*x^5 - 10*x^4 + 41*x^3 - 10*x^2 - 16*x - 3 over Rational Field
with equations :
-1/4*X^2*T^4 - 1/4*X*T^5 - 3/4*T^6
-13/64*X^6*T^12 + 15/64*X^5*T^13 - 3/16*X^4*T^14 + 19/64*X^3*T^15 -
    1/32*X^2*Y*T^15 + 3/16*X^2*T^16 - 1/8*X*Y*T^16 + 15/64*X*T^17 + 1/32*Y*T^17
    + 13/64*T^18
3/4*X^2*T^4 - 1/4*X*T^5 + 1/4*T^6, [
    [
        $.1 - 1/2*$.3,
        -25/16*$.2,
        -1/2*$.1 - $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 35 ], Hyperelliptic Curve defined by y^2 = -x^6 + 3*x^5 + 88*x^4 - 181*x^3
    + 24*x^2 + 67*x - 23 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 = -x^6 + 3*x^5 + 88*x^4 -
    181*x^3 + 24*x^2 + 67*x - 23 over Rational Field
with equations :
X*T^2 - 1/2*T^3
-1/8*X^2*Y*T^6 + 1/8*X*Y*T^7 + 1/8*Y*T^8
-1/2*X^2*T - 1/2*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        1/2*$.1 + $.3,
        -25/16*$.2,
        $.1 - 1/2*$.3
    ]
]>
<[ 1, 14 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 7 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -5*x^6 - 3*x^5 -
    12*x^4 + 37*x^3 + 3*x^2 + 42*x - 92 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y =
    -5*x^6 - 3*x^5 - 12*x^4 + 37*x^3 + 3*x^2 + 42*x - 92 over Rational Field
with equations :
X*T^4
-1/32*X^5*T^10 + 1/16*X^4*T^11 + 5/32*X^3*T^12 - 1/32*X^2*Y*T^12 - 1/16*X^2*T^13
    - 1/32*X*T^14 - 1/32*Y*T^14
-1/4*X^2*T^3 - 1/4*X*T^4 + 1/4*T^5, [
    [
        -$.3,
        -$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 10 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
23*x[1]^2 + 1168/7*x[1]*x[2] + 13802/49*x[2]^2 - 36688/343*x[2]*x[3] -
    16721/2401*x[3]^2 + x[4]^2, 1, <0, "C_2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
23*x[1]^2 + 1168/7*x[1]*x[2] + 13802/49*x[2]^2 - 36688/343*x[2]*x[3] -
    16721/2401*x[3]^2 + x[4]^2
with equations :
X^4 + 2/7*X^3*T + 92/49*X^2*T^2 + 13/49*X*T^3 + 169/196*T^4
X^3*T - 5/14*X^2*T^2 + 6/7*X*T^3 - 13/28*T^4
X^2*T^2 - X*T^3 + 1/4*T^4
-Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        1/2*$.1 + $.3,
        25/16*$.2,
        $.1 - 1/2*$.3
    ]
]>
<[ 1, 2 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
23*x[1]^2 - 180*x[1]*x[2] + 450*x[2]^2 - 708*x[2]*x[3] + 1439*x[3]^2 + x[4]^2,
1, <0, "C_2^2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
23*x[1]^2 - 180*x[1]*x[2] + 450*x[2]^2 - 708*x[2]*x[3] + 1439*x[3]^2 + x[4]^2
with equations :
X^4 - 2*X^2*T^2 + T^4
-X^3*T + X*T^3
X^2*T^2
Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        $.2,
        $.1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, -2, 0, -1, 0, -1/2, 0, 0 ]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
quotient genus >= 2
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, 2, 0, -1, 0, 1/2, 0, 0 ]) >
quotient genus = 1
quotient genus >= 2
making ShimDB object
<[ 1, 5 ], Hyperelliptic Curve defined by y^2 = -3*x^5 + 5*x^4 - x^3 - 37*x^2 +
    24*x + 12 over Rational Field, 2, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 = -3*x^5 + 5*x^4 - x^3 - 37*x^2 + 24*x + 12
over Rational Field
with equations :
X^2 + T^2
-X*Y*T^4
T^2, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 15 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 30 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
3*x[1]^2 - 14*x[2]^2 - 5*x[3]^2 + x[4]^2, 1, <0, "C_4">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
3*x[1]^2 - 14*x[2]^2 - 5*x[3]^2 + x[4]^2
with equations :
X^4 + 4*X^2*T^2 + 4*T^4
-X^3*T - 2*X*T^3
X^2*T^2
Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -2*$.3,
        4*$.2,
        -$.1
    ]
]>
<[ 1, 3 ], Elliptic Curve defined by y^2 + x*y + y = x^3 - 14*x - 64 over
Rational Field, 1, <0, "C_2">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + x*y + y = x^3
- 14*x - 64 over Rational Field
with equations :
-7*X^4 - 22*X^2*T^2 - 3*T^4
3*X^4 + 8*X^2*T^2 + 10*Y*T^3 - 3*T^4
X^4 + 6*X^2*T^2 + 9*T^4, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = -3*x^6 - 9*x^5
    - 26*x^4 - 37*x^3 - 47*x^2 - 30*x - 16 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y =
    -3*x^6 - 9*x^5 - 26*x^4 - 37*x^3 - 47*x^2 - 30*x - 16 over Rational Field
with equations :
1/2*X^2*T^3 - 1/2*X*T^4 - T^5
-1/8*X^5*T^10 + 1/8*X^3*T^12 - 1/8*X^2*Y*T^12 - 1/2*X*T^14 - 1/4*Y*T^14
X*T^4, [
    [
        -2*$.3,
        -4*$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 10 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
3*x[1]^2 + 34*x[2]^2 + 75*x[3]^2 + x[4]^2, 1, <0, "C_2\\times C_4">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
3*x[1]^2 + 34*x[2]^2 + 75*x[3]^2 + x[4]^2
with equations :
X^4 - 4*X^2*T^2 + 4*T^4
-X^3*T + 2*X*T^3
X^2*T^2
Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        2*$.3,
        4*$.2,
        -$.1
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -2*x^6 - 8*x^5 -
    9*x^4 - 3*x^3 - 9*x^2 - 8*x - 2 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -2*x^6 -
    8*x^5 - 9*x^4 - 3*x^3 - 9*x^2 - 8*x - 2 over Rational Field
with equations :
1/2*X^2*T^3 + 1/2*X*T^4 + T^5
-3/8*X^5*T^10 - 13/8*X^3*T^12 - 1/8*X^2*Y*T^12 - 3/2*X*T^14 + 1/4*Y*T^14
-1/2*X^2*T^3 + 1/2*X*T^4 - T^5, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        2*$.3,
        -4*$.2,
        $.1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, -2, 0, -1, 0, -1/2, 0, 0 ]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
quotient genus >= 2
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, 2, 0, -1, 0, 1/2, 0, 0 ]) >
quotient genus = 1
quotient genus >= 2
making ShimDB object
<[ 1, 5 ], Hyperelliptic Curve defined by y^2 = -3*x^5 + 5*x^4 - x^3 - 37*x^2 +
    24*x + 12 over Rational Field, 2, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 = -3*x^5 + 5*x^4 - x^3 - 37*x^2 + 24*x + 12
over Rational Field
with equations :
X^2 + T^2
-X*Y*T^4
T^2, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 15 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 30 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
3*x[1]^2 - 14*x[2]^2 - 5*x[3]^2 + x[4]^2, 1, <0, "C_4">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
3*x[1]^2 - 14*x[2]^2 - 5*x[3]^2 + x[4]^2
with equations :
X^4 + 4*X^2*T^2 + 4*T^4
-X^3*T - 2*X*T^3
X^2*T^2
Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -2*$.3,
        4*$.2,
        -$.1
    ]
]>
<[ 1, 3 ], Elliptic Curve defined by y^2 + x*y + y = x^3 - 14*x - 64 over
Rational Field, 1, <0, "C_2">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + x*y + y = x^3
- 14*x - 64 over Rational Field
with equations :
-7*X^4 - 22*X^2*T^2 - 3*T^4
3*X^4 + 8*X^2*T^2 + 10*Y*T^3 - 3*T^4
X^4 + 6*X^2*T^2 + 9*T^4, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = -3*x^6 - 9*x^5
    - 26*x^4 - 37*x^3 - 47*x^2 - 30*x - 16 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y =
    -3*x^6 - 9*x^5 - 26*x^4 - 37*x^3 - 47*x^2 - 30*x - 16 over Rational Field
with equations :
1/2*X^2*T^3 - 1/2*X*T^4 - T^5
-1/8*X^5*T^10 + 1/8*X^3*T^12 - 1/8*X^2*Y*T^12 - 1/2*X*T^14 - 1/4*Y*T^14
X*T^4, [
    [
        -2*$.3,
        -4*$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 10 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
3*x[1]^2 + 34*x[2]^2 + 75*x[3]^2 + x[4]^2, 1, <0, "C_2\\times C_4">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
3*x[1]^2 + 34*x[2]^2 + 75*x[3]^2 + x[4]^2
with equations :
X^4 - 4*X^2*T^2 + 4*T^4
-X^3*T + 2*X*T^3
X^2*T^2
Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        2*$.3,
        4*$.2,
        -$.1
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -2*x^6 - 8*x^5 -
    9*x^4 - 3*x^3 - 9*x^2 - 8*x - 2 over Rational Field, 2, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -2*x^6 -
    8*x^5 - 9*x^4 - 3*x^3 - 9*x^2 - 8*x - 2 over Rational Field
with equations :
1/2*X^2*T^3 + 1/2*X*T^4 + T^5
-3/8*X^5*T^10 - 13/8*X^3*T^12 - 1/8*X^2*Y*T^12 - 3/2*X*T^14 + 1/4*Y*T^14
-1/2*X^2*T^3 + 1/2*X*T^4 - T^5, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        2*$.3,
        -4*$.2,
        $.1
    ]
]>

computing GYData
making data-quotient list
non-hyperelliptic case
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [1, -1, -1]) >
quotient genus = 1
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, -1, 1]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
making ShimDB object
<[ 1, 21 ], Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 4*x + 5 over
Rational Field, 1, <0, "C_8">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + x*y + y = x^3
+ x^2 - 4*x + 5 over Rational Field
with equations :
Z1^5 + 8/3*X1*Z1^3*T1 + 16/3*Z1^3*T1^2 + 224/27*X1*Z1*T1^3 + 560/81*Z1*T1^4
-Z1^5 - 4/3*X1*Z1^3*T1 + 2/3*Y1*Z1^2*T1^2 - 52/9*Z1^3*T1^2 + 4/9*X1*Y1*T1^3 -
    112/27*X1*Z1*T1^3 + 52/27*Y1*T1^4 - 224/27*Z1*T1^4
Z1^5 + 56/9*Z1^3*T1^2 + 784/81*Z1*T1^4, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        -Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 14 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = 15*x^6 + 18*x^5 +
    11*x^4 - 5*x^3 + 11*x^2 + 18*x + 15 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y =
    15*x^6 + 18*x^5 + 11*x^4 - 5*x^3 + 11*x^2 + 18*x + 15 over Rational Field
with equations :
-1/4*X1*Z1^2*T1^6 + 1/2*Z1^3*T1^6 + 3/2*Z1*T1^8
-5/64*X1*Z1^8*T1^18 - 27/64*X1*Z1^6*T1^20 + 9/32*X1*Y1*Z1^4*T1^21 -
    9/16*X1*Z1^4*T1^22 + 27/32*X1*Y1*Z1^2*T1^23
-1/4*X1*Z1^2*T1^6 - 1/2*Z1^3*T1^6 - 3/2*Z1*T1^8, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 = -4*x^6 + 7*x^4 + 15*x^3 + 7*x^2
    - 4 over Rational Field, 2, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 = -4*x^6 + 7*x^4 + 15*x^3 + 7*x^2 - 4 over
Rational Field
with equations :
1/2*Z1^2*T1^2 - 1/2*X1*T1^3 + 3/2*T1^4
-1/8*X1*Y1*Z1^2*T1^8 - 3/8*X1*Y1*T1^10
-1/2*Z1^2*T1^2 - 1/2*X1*T1^3 - 3/2*T1^4, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 7 ], Conic over Rational Field defined by
$.1^2 + 3*$.2^2 + $.3^2, 0, 0, 0, 0>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -7*x^5 - 4*x^4 -
    15*x^3 - 4*x^2 - 7*x over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -7*x^5 - 4*x^4 -
    15*x^3 - 4*x^2 - 7*x over Rational Field
with equations :
-1/4*Z1^2*T1^4 + 1/2*Z1*T1^5
1/64*Z1^6*T1^12 + 1/32*X1*Y1*Z1^2*T1^14 - 1/16*Z1^4*T1^14
-1/4*Z1^2*T1^4 - 1/2*Z1*T1^5, [
    [
        -X1,
        -Y1,
        Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 42 ], Elliptic Curve defined by y^2 + x*y = x^3 + x over Rational Field,
1, <0, "C_4">, Mapping from: Crv: top_curve to Elliptic Curve defined by y^2 + x*y = x^3 + x
over Rational Field
with equations :
Z1^3 - 4*Z1*T1^2
-1/2*Z1^3 + 1/2*Y1*T1^2 + 2*Z1*T1^2
Z1^3 - 4*Z1^2*T1 + 4*Z1*T1^2, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 2 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
7/81*x[1]^2 + 200/81*x[2]^2 + 112/81*x[3]^2 + x[4]^2, 1, <0, "C_2\\times C_4">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
7/81*x[1]^2 + 200/81*x[2]^2 + 112/81*x[3]^2 + x[4]^2
with equations :
Z1^3
X1*Z1^2
-Z1^3 - 3*Z1*T1^2
-1/3*Y1*T1^2, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        -Y1,
        -Z1,
        T1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, 1, 0, -1, 0, 1, 0, 0 ]) >
quotient genus = 1
quotient genus >= 2
MatrixGroup<3, RationalField() |
    Matrix(RationalField(), 3, 3, [ 0, 0, -1, 0, -1, 0, -1, 0, 0 ]) >
quotient genus = 1
MatrixGroup<3, RationalField() |
    DiagonalMatrix(RationalField(), [-1, 1, -1]) >
quotient genus = 1
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 33 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
27*x[1]^2 + 416*x[2]^2 + 2816*x[3]^2 + x[4]^2, 1, <0, "C_6">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
27*x[1]^2 + 416*x[2]^2 + 2816*x[3]^2 + x[4]^2
with equations :
X^4 - 2*X^2*T^2 + T^4
-X^3*T + X*T^3
X^2*T^2
Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        $.2,
        $.1
    ]
]>
<[ 1, 22 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = -11*x^6 +
    33*x^5 - 15*x^4 - 26*x^3 + 7*x^2 + 10*x + 2 over Rational Field, 2, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x +
    1)*y = -11*x^6 + 33*x^5 - 15*x^4 - 26*x^3 + 7*x^2 + 10*x + 2 over Rational
Field
with equations :
-1/8*X^2*T^4 - 3/8*T^6
-3/512*X^6*T^12 + 9/512*X^4*T^14 - 25/512*X^2*T^16 - 1/128*X*Y*T^16 +
    19/512*T^18
1/4*X^2*T^4 - 1/4*T^6, [
    [
        -$.1,
        -$.2,
        $.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 11 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
27*x[1]^2 + 200*x[2]^2 + 1584*x[3]^2 + x[4]^2, 1, <0, "C_{10}">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
27*x[1]^2 + 200*x[2]^2 + 1584*x[3]^2 + x[4]^2
with equations :
X^4 + 2*X^2*T^2 + T^4
-X^3*T - X*T^3
X^2*T^2
Y*T^3, [
    [
        $.3,
        $.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 3 ], Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
108*x[1]^2 - 1232*x[1]*x[2] + 8584*x[2]^2 - 1232*x[2]*x[3] + 108*x[3]^2 +
    x[4]^2, 1, <0, "C_2^2">, Mapping from: Crv: top_curve to Curve over Rational Field defined by
x[2]^2 - x[1]*x[3],
108*x[1]^2 - 1232*x[1]*x[2] + 8584*x[2]^2 - 1232*x[2]*x[3] + 108*x[3]^2 + x[4]^2
with equations :
X^4
-X^2*T^2
T^4
2*Y*T^3, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1,
        $.2,
        $.3
    ]
]>
<[ 1, 66 ], Conic over Rational Field defined by
-$.2^2 + $.1*$.3, 0, 0, 0, 0>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 = -11*x^5 + 18*x^4 - 41*x^3 +
    18*x^2 - 11*x over Rational Field, 2, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 = -11*x^5 + 18*x^4 - 41*x^3 + 18*x^2 - 11*x
over Rational Field
with equations :
-1/4*X^2*T + 1/2*X*T^2 - 1/4*T^3
-1/64*X^2*Y*T^6 + 1/64*Y*T^8
-1/4*X^2*T - 1/2*X*T^2 - 1/4*T^3, [
    [
        $.3,
        -$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -5*x^6 + 11*x^5 -
    25*x^4 + 26*x^3 - 25*x^2 + 11*x - 5 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y =
    -5*x^6 + 11*x^5 - 25*x^4 + 26*x^3 - 25*x^2 + 11*x - 5 over Rational Field
with equations :
-1/8*X^2*T^3 - 1/2*X*T^4 + 1/8*T^5
-1/128*X^5*T^10 + 9/64*X^3*T^12 - 1/256*X^2*Y*T^12 - 1/128*X*T^14 - 1/256*Y*T^14
1/8*X^2*T^3 - 1/2*X*T^4 - 1/8*T^5, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.3,
        -$.2,
        $.1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 5 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = -11*x^6 +
    33*x^5 - 78*x^4 + 100*x^3 - 107*x^2 + 61*x - 29 over Rational Field, 2, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x +
    1)*y = -11*x^6 + 33*x^5 - 78*x^4 + 100*x^3 - 107*x^2 + 61*x - 29 over
Rational Field
with equations :
1/2*X^2*T^3 + 1/2*X*T^4 - 1/2*T^5
-1/8*X^5*T^10 - 1/2*X^4*T^11 - 5/8*X^3*T^12 + 1/2*X^2*T^13 - 1/8*X*T^14 -
    1/8*Y*T^14
X*T^4, [
    [
        -$.3,
        -$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 55 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^2)*y = -3*x^8 + 7*x^6
    + 9*x^4 + 14*x^2 + 20 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^4 + x^2)*y = -3*x^8 + 7*x^6
    + 9*x^4 + 14*x^2 + 20 over Rational Field
with equations :
X^2*T^6 + T^8
-1/2*X^8*T^24 - 5/2*X^6*T^26 - 4*X^4*T^28 + 1/2*X^2*Y*T^29 - 5/2*X^2*T^30 -
    1/2*Y*T^31 - 1/2*T^32
-X*T^7, [
    [
        $.3,
        -$.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 110 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 22 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^2)*y = -3*x^8 - 48*x^6
    - 311*x^4 - 915*x^2 - 1024 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^4 + x^2)*y = -3*x^8 -
    48*x^6 - 311*x^4 - 915*x^2 - 1024 over Rational Field
with equations :
X^2*T^6 - T^8
-1/2*X^8*T^24 + 3/2*X^6*T^26 - 2*X^4*T^28 + 1/2*X^2*Y*T^29 + 3/2*X^2*T^30 +
    1/2*Y*T^31 - 1/2*T^32
-X*T^7, [
    [
        -$.3,
        $.2,
        $.1
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 11 ], Hyperelliptic Curve defined by y^2 + (x^2 + x + 1)*y = 5*x^6 +
    15*x^5 + 10*x^4 - 5*x^3 - 2*x^2 + 3*x - 3 over Rational Field, 2, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x +
    1)*y = 5*x^6 + 15*x^5 + 10*x^4 - 5*x^3 - 2*x^2 + 3*x - 3 over Rational Field
with equations :
T^6
1/2*X^6*T^12 + X^4*T^14 + X^2*T^16 - 1/2*Y*T^17 + 1/2*T^18
-X^2*T^4 - T^6, [
    [
        $.1,
        $.2,
        -$.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 10 ], Hyperelliptic Curve defined by y^2 = 11*x^7 - 80*x^6 + 240*x^5 -
    362*x^4 + 240*x^3 - 80*x^2 + 11*x over Rational Field, 3, -1, Mapping from:
Crv: top_curve to Hyperelliptic Curve defined by y^2 = 11*x^7 - 80*x^6 + 240*x^5
    - 362*x^4 + 240*x^3 - 80*x^2 + 11*x over Rational Field
with equations :
X^2
X*Y*T^6
-T^2, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        $.1,
        -$.2,
        -$.3
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -x^6 - x^5 - 7*x^4
    - 3*x^3 - 7*x^2 - x - 1 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -x^6 - x^5 -
    7*x^4 - 3*x^3 - 7*x^2 - x - 1 over Rational Field
with equations :
-1/2*X^2*T^3 - 1/2*X*T^4 - 1/2*T^5
-1/8*X^5*T^10 - 1/8*X^3*T^12 - 1/8*X*T^14 - 1/8*Y*T^14
1/2*X^2*T^3 - 1/2*X*T^4 + 1/2*T^5, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        $.3,
        $.2,
        $.1
    ]
]>

computing GYData
making data-quotient list
non-hyperelliptic case
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 26 ], Conic over Rational Field defined by
$.1^2 + 24*$.2^2 + 8*$.3^2, 0, 0, 0, 0>
<[ 1, 13 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = 2*x^8 + 57*x^6 +
    601*x^4 + 2721*x^2 + 4394 over Rational Field, 3, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = 2*x^8 + 57*x^6 +
    601*x^4 + 2721*x^2 + 4394 over Rational Field
with equations :
X1*Z1*T1^6
7/1024*X1*Z1^7*T1^24 + 39/1024*X1*Z1^5*T1^26 - 9/128*Y1*Z1^4*T1^27 +
    45/1024*X1*Z1^3*T1^28 - 27/64*Y1*Z1^2*T1^29 - 27/1024*X1*Z1*T1^30 -
    81/128*Y1*T1^31
1/8*Z1^2*T1^6 + 3/8*T1^8, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 39 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^2 + 1)*y = x^7 + 3*x^6
    + 7*x^5 + 19*x^4 + 29*x^3 + 19*x^2 + 6*x - 6 over Rational Field, 3, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^4 + x^2
    + 1)*y = x^7 + 3*x^6 + 7*x^5 + 19*x^4 + 29*x^3 + 19*x^2 + 6*x - 6 over
Rational Field
with equations :
-1/2*Z1*T1^3 - 1/2*T1^4
-1/32*Z1^4*T1^12 - 1/8*Z1^3*T1^13 + 2*X1*Y1*T1^14 - 5/16*Z1^2*T1^14 -
    3/8*Z1*T1^15 - 21/32*T1^16
T1^4, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        -Y1,
        Z1,
        T1
    ]
]>
<[ 1, 78 ], Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -x^5 + 2*x^4 -
    2*x^3 + 2*x^2 - x over Rational Field, 2, -1, Mapping from: Crv: top_curve
to Hyperelliptic Curve defined by y^2 + (x^3 + 1)*y = -x^5 + 2*x^4 - 2*x^3 +
    2*x^2 - x over Rational Field
with equations :
1/16*Z1^2*T1^4 - 1/2*X1*T1^5 + 3/16*T1^6
-1/4096*Z1^6*T1^12 + 1/64*X1*Y1*Z1^2*T1^14 + 15/4096*Z1^4*T1^14 +
    3/64*X1*Y1*T1^16 + 117/4096*Z1^2*T1^16 + 189/4096*T1^18
1/16*Z1^2*T1^4 + 1/2*X1*T1^5 + 3/16*T1^6, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^8 + 3*x^6 -
    17*x^4 - 23*x^2 - 6 over Rational Field, 3, -1, Mapping from: Crv: top_curve
to Hyperelliptic Curve defined by y^2 + (x^3 + x)*y = -2*x^8 + 3*x^6 - 17*x^4 -
    23*x^2 - 6 over Rational Field
with equations :
-1/8*Z1^2*T1^5 - 3/8*T1^7
1/1024*X1*Z1^6*T1^21 + 1/128*Y1*Z1^5*T1^22 + 1/1024*X1*Z1^4*T1^23 +
    3/64*Y1*Z1^3*T1^24 - 21/1024*X1*Z1^2*T1^25 + 9/128*Y1*Z1*T1^26 -
    45/1024*X1*T1^27
X1*T1^6, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        -Y1,
        -Z1,
        T1
    ]
]>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 = -2*x^6 + 6*x^5 - 20*x^4 + 30*x^3
    - 108*x^2 + 94*x + 46 over Rational Field, 2, -1, Mapping from: Crv:
top_curve to Hyperelliptic Curve defined by y^2 = -2*x^6 + 6*x^5 - 20*x^4 +
    30*x^3 - 108*x^2 + 94*x + 46 over Rational Field
with equations :
1/2*Z1 + 1/2*T1
4*Y1*T1^2
T1, [
    [
        -X1,
        Y1,
        Z1,
        T1
    ],
    [
        X1,
        Y1,
        Z1,
        T1
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = -2*x^6 - 2*x^5 -
    26*x^4 - 21*x^3 - 111*x^2 - 49*x - 149 over Rational Field, 2, -1, Mapping
from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^2 + x)*y =
    -2*x^6 - 2*x^5 - 26*x^4 - 21*x^3 - 111*x^2 - 49*x - 149 over Rational Field
with equations :
1/6*X1*Z1*T1^4 - 5/48*Z1^2*T1^4 - 5/16*T1^6
1/1152*X1*Z1^5*T1^12 + 13/36864*Z1^6*T1^12 + 1/64*X1*Y1*Z1^2*T1^14 +
    1/192*X1*Z1^3*T1^14 + 31/12288*Z1^4*T1^14 + 3/64*X1*Y1*T1^16 +
    1/128*X1*Z1*T1^16 + 23/4096*Z1^2*T1^16 + 15/4096*T1^18
-1/6*X1*Z1*T1^4 - 1/48*Z1^2*T1^4 - 1/16*T1^6, [
    [
        X1,
        Y1,
        Z1,
        T1
    ],
    [
        -X1,
        -Y1,
        -Z1,
        T1
    ]
]>

computing GYData
making data-quotient list
hyperelliptic case
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
quotient genus >= 2
making ShimDB object
<[ 1, 26 ], Hyperelliptic Curve defined by y^2 + (x^5 + 1)*y = -2*x^10 - 16*x^9
    - 61*x^8 - 135*x^7 - 202*x^6 - 222*x^5 - 202*x^4 - 135*x^3 - 61*x^2 - 16*x -
    2 over Rational Field, 4, -1, Mapping from: Crv: top_curve to Hyperelliptic
Curve defined by y^2 + (x^5 + 1)*y = -2*x^10 - 16*x^9 - 61*x^8 - 135*x^7 -
    202*x^6 - 222*x^5 - 202*x^4 - 135*x^3 - 61*x^2 - 16*x - 2 over Rational
Field
with equations :
2/3*X^2*T^8 + X*T^9 + 2/3*T^10
-31/486*X^10*T^40 - 25/54*X^9*T^41 - 385/243*X^8*T^42 - 85/27*X^7*T^43 -
    1645/486*X^6*T^44 + 1645/243*X^4*T^46 + 340/27*X^3*T^47 - 1/54*X^2*Y*T^47 +
    3080/243*X^2*T^48 - 2/27*X*Y*T^48 + 200/27*X*T^49 - 1/27*Y*T^49 +
    496/243*T^50
-1/3*X^2*T^8 - X*T^9 - 4/3*T^10, [
    [
        -2*$.1 - 2*$.3,
        -16*$.2,
        $.1 + 2*$.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 13 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^3 + x^2)*y = -x^8 +
    4*x^7 - 16*x^6 + 28*x^5 - 47*x^4 + 48*x^3 - 46*x^2 + 24*x - 12 over Rational
Field, 3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2
+ (x^4 + x^3 + x^2)*y = -x^8 + 4*x^7 - 16*x^6 + 28*x^5 - 47*x^4 + 48*x^3 -
    46*x^2 + 24*x - 12 over Rational Field
with equations :
1/3*X^2*T^6 - 2/3*T^8
-1/54*X^8*T^24 - 1/18*X^7*T^25 + 1/27*X^6*T^26 + 2/9*X^5*T^27 + 1/18*X^4*T^28 -
    2/9*X^3*T^29 - 2/27*X^2*T^30 + 1/54*Y*T^31 - 2/27*T^32
1/3*X^2*T^6 + X*T^7 + 1/3*T^8, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1 - 2*$.3,
        $.2,
        $.1 + $.3
    ]
]>
<[ 1, 39 ], Conic over Rational Field defined by
$.2^2 - $.1*$.3, 0, 0, 0, 0>
<[ 1, 78 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^3 + x^2 + x + 1)*y =
    -2*x^8 + 11*x^7 - 28*x^6 + 20*x^5 - 5*x^4 + 20*x^3 - 28*x^2 + 11*x - 2 over
Rational Field, 3, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve
defined by y^2 + (x^4 + x^3 + x^2 + x + 1)*y = -2*x^8 + 11*x^7 - 28*x^6 + 20*x^5
    - 5*x^4 + 20*x^3 - 28*x^2 + 11*x - 2 over Rational Field
with equations :
-X*T^7
-1/2*X^8*T^24 - 13/2*X^7*T^25 - 36*X^6*T^26 - 110*X^5*T^27 - 401/2*X^4*T^28 -
    220*X^3*T^29 - 144*X^2*T^30 - 52*X*T^31 - 1/2*Y*T^31 - 8*T^32
-X^2*T^6 - 3*X*T^7 - 2*T^8, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        2*$.3,
        16*$.2,
        $.1
    ]
]>
<[ 1, 3 ], Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3)*y = -4*x^10 -
    26*x^9 - 101*x^8 - 240*x^7 - 470*x^6 - 655*x^5 - 796*x^4 - 688*x^3 - 524*x^2
    - 240*x - 96 over Rational Field, 4, -1, Mapping from: Crv: top_curve to
Hyperelliptic Curve defined by y^2 + (x^5 + x^4 + x^3)*y = -4*x^10 - 26*x^9 -
    101*x^8 - 240*x^7 - 470*x^6 - 655*x^5 - 796*x^4 - 688*x^3 - 524*x^2 - 240*x
    - 96 over Rational Field
with equations :
1/3*X^2*T^8 - 2/3*T^10
-1/486*X^10*T^40 - 1/162*X^9*T^41 - 1/243*X^8*T^42 + 1/81*X^7*T^43 +
    29/486*X^6*T^44 + 2/27*X^5*T^45 - 23/243*X^4*T^46 - 20/81*X^3*T^47 -
    1/54*X^2*Y*T^47 - 10/243*X^2*T^48 - 1/27*X*Y*T^48 + 16/81*X*T^49 -
    1/27*Y*T^49 + 28/243*T^50
-1/3*X^2*T^8 - X*T^9 - 1/3*T^10, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        -$.1 - 2*$.3,
        -$.2,
        $.1 + $.3
    ]
]>
<[ 1, 6 ], Hyperelliptic Curve defined by y^2 + (x^4 + x^3 + x^2 + x + 1)*y =
    x^7 + 3*x^6 + 5*x^5 + 5*x^4 + 5*x^3 + 3*x^2 + x over Rational Field, 3, -1,
Mapping from: Crv: top_curve to Hyperelliptic Curve defined by y^2 + (x^4 + x^3
    + x^2 + x + 1)*y = x^7 + 3*x^6 + 5*x^5 + 5*x^4 + 5*x^3 + 3*x^2 + x over
Rational Field
with equations :
1/3*X^2*T^6 + X*T^7 + 4/3*T^8
-11/162*X^8*T^24 - 7/18*X^7*T^25 - 91/81*X^6*T^26 - 20/9*X^5*T^27 -
    187/54*X^4*T^28 - 40/9*X^3*T^29 - 364/81*X^2*T^30 - 28/9*X*T^31 +
    1/54*Y*T^31 - 88/81*T^32
-2/3*X^2*T^6 - X*T^7 - 2/3*T^8, [
    [
        -2*$.1 - 2*$.3,
        16*$.2,
        $.1 + 2*$.3
    ],
    [
        $.1,
        $.2,
        $.3
    ]
]>
<[ 1, 2 ], Hyperelliptic Curve defined by y^2 + (x^5 + 1)*y = -2*x^10 + 22*x^9 -
    98*x^8 + 196*x^7 - 157*x^6 + 64*x^5 - 157*x^4 + 196*x^3 - 98*x^2 + 22*x - 2
over Rational Field, 4, -1, Mapping from: Crv: top_curve to Hyperelliptic Curve 
defined by y^2 + (x^5 + 1)*y = -2*x^10 + 22*x^9 - 98*x^8 + 196*x^7 - 157*x^6 +
    64*x^5 - 157*x^4 + 196*x^3 - 98*x^2 + 22*x - 2 over Rational Field
with equations :
-X*T^9
1/2*X^10*T^40 + 15/2*X^9*T^41 + 50*X^8*T^42 + 195*X^7*T^43 + 985/2*X^6*T^44 +
    842*X^5*T^45 + 985*X^4*T^46 + 780*X^3*T^47 + 1/2*X^2*Y*T^47 + 400*X^2*T^48 +
    120*X*T^49 - Y*T^49 + 16*T^50
-X^2*T^8 - 3*X*T^9 - 2*T^10, [
    [
        $.1,
        $.2,
        $.3
    ],
    [
        2*$.3,
        -16*$.2,
        $.1
    ]
]>

Index Name                                                 Time        Count
1     <main>                                               49.69       1
16    WriteShimToFile(<RngIntElt> D, <RngIntElt> N) -> .   49.69       42
19    DataToQuotientList(<Any> curve_data) -> .            49.39       42
12    Constructor (sub)                                    22.66       552232
177   ReducedMinimalWeierstrassModel(<CrvHyp> C) -> CrvHyp, MapIsoSch
                                                           22.44       266
265   ReducedModel(<CrvHyp> C) -> CrvHyp, MapIsoSch        14.95       266
271   Roots(<RngUPolElt> f, <Rng> S) -> SeqEnum            14.25       1521
267   Reduce(<RngIntElt> d, <RngUPolElt> pol) -> RngUPolElt, GrpMatElt
                                                           14.12       266
625   CurveQuotient(<GrpAutCrv> G) -> Crv, MapSch          13.65       162
23    IsHyperelliptic(<Crv> C) -> BoolElt, CrvHyp, MapSch  10.87       34
273   InternalComplexRoots(<RngUPolElt> f, <RngIntElt> p) -> SeqEnum
                                                           10.44       872
287   roots                                                9.51        1124
384   Covariant(<RngIntElt> d, <RngUPolElt> pol) -> FldComElt, FldComElt
                                                           8.90        395
446   AutomorphismGroup(<Crv> C, <SeqEnum> phis) -> GrpAutCrv8.88        162
180   MinimalWeierstrassModel(<CrvHyp> C) -> CrvHyp, MapIsoSch7.49        266
223   pMinimalWeierstrassModel(<CrvHyp> C, <RngIntElt> p) -> CrvHyp, MapIsoSch
                                                           7.18        397
230   pMinimalWeierstrassModelfunction                     7.15        439
558   build_auto_group                                     6.80        162
31    MapToConic                                           6.43        74
244   MinimalWeierstrassModel2                             6.36        266

Total time: 50.119 seconds, Total memory usage: 216.75MB