32S7-8,2,8-g5

graph data
Name 32S7-8,2,8-g5
Type Hyperbolic
Degree 32
Genus 5
Galois orbit size for 32S7-8,2,8-g5-path1 1
Galois orbit size for 32S7-8,2,8-g5-path10 1
Galois orbit size for 32S7-8,2,8-g5-path11 1
Galois orbit size for 32S7-8,2,8-g5-path2 1
Galois orbit size for 32S7-8,2,8-g5-path3 1
Galois orbit size for 32S7-8,2,8-g5-path4 1
Galois orbit size for 32S7-8,2,8-g5-path5 1
Galois orbit size for 32S7-8,2,8-g5-path6 1
Galois orbit size for 32S7-8,2,8-g5-path7 1
Galois orbit size for 32S7-8,2,8-g5-path8 1
Galois orbit size for 32S7-8,2,8-g5-path9 1
Passport size 1
Pointed size 1

Above

64S14-8,4,8-g17 64S12-8,2,8-g9 64S24-8,4,8-g17 64S10-8,2,8-g9 64S4-8,2,8-g9 64S4-8,4,8-g17 64S10-8,4,8-g17

Below

16T10-4,2,4-g1

Belyi Curve 1: 32S7-8,2,8-g5-path10

\(-2x_{1}^{2} + x_{2}^{3} + x_{2}2\)
\(x_{1}x_{3}^{2} - 1/2x_{2}^{2} + 1/2\)

Belyi Curve 1 Base Field: Rationals

Belyi Curve 1 Degree: 9

Belyi Curve 1 Naive Measure: 9

Belyi Map 1 Numerator:

\(-x_{3}^{8}\)

Belyi Map 1 Denominator:

\(4\)

Belyi Curve 2: 32S7-8,2,8-g5-path11

\(-2x_{1}^{2} + x_{2}^{3} + x_{2}2\)
\(x_{1}x_{3}^{2} + 1/4(-\nu - 1)x_{2}^{2} + 1/4(\nu + 1)\)

Belyi Curve 2 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 2 Degree: 9

Belyi Curve 2 Naive Measure: 13

Belyi Map 2 Numerator:

\(1\)

Belyi Map 2 Denominator:

\(x_{3}^{8}\)

Belyi Curve 3: 32S7-8,2,8-g5-path2

\(-2x_{1}^{2} + x_{2}^{3} + x_{2}2\)
\(x_{1}x_{3}^{2} - 1/2x_{2}^{2} + 1/2\)

Belyi Curve 3 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 3 Degree: 9

Belyi Curve 3 Naive Measure: 9

Belyi Map 3 Numerator:

\(-4\)

Belyi Map 3 Denominator:

\(x_{3}^{8}\)

Belyi Curve 4: 32S7-8,2,8-g5-path3

\(x_{1}x_{4}^{2} - x_{2}x_{3} - x_{3}3\)
\(-x_{1}x_{3} + x_{2}x_{4}^{2} - x_{4}^{2}\)
\(x_{1}^{2} - x_{2}^{2} + 1\)
\(-x_{2} + x_{3}^{2}\)

Belyi Curve 4 Base Field: Rationals

Belyi Curve 4 Degree: 10

Belyi Curve 4 Naive Measure: 11

Belyi Map 4 Numerator:

\(-x_{3}^{2}x_{4}^{12} + 5x_{3}^{2}x_{4}^{8} - 3x_{3}^{2}x_{4}^{4} - x_{3}^{2} + x_{4}^{12} - 3x_{4}^{8} - x_{4}^{4} - 1\)

Belyi Map 4 Denominator:

\(4x_{3}^{2}x_{4}^{4} - 4x_{3}^{2} - 4x_{4}^{4}\)

Belyi Curve 5: 32S7-8,2,8-g5-path8

\(-2x_{1}^{2} + x_{2}^{3} - x_{2}2\)
\(x_{1}x_{3}^{2} - 1/2x_{2}^{2} - 1/2\)

Belyi Curve 5 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 5 Degree: 9

Belyi Curve 5 Naive Measure: 9

Belyi Map 5 Numerator:

\(1/4x_{3}^{8}\)

Belyi Map 5 Denominator:

\(1\)

Belyi Curve 6: 32S7-8,2,8-g5-path9

\(-2x_{1}^{2} + x_{2}^{3} - x_{2}2\)
\(x_{1}x_{3}^{2} - 1/2x_{2}^{2} - 1/2\)

Belyi Curve 6 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 6 Degree: 9

Belyi Curve 6 Naive Measure: 9

Belyi Map 6 Numerator:

\(1/4x_{3}^{8}\)

Belyi Map 6 Denominator:

\(1\)