32S5-8,8,2-g5

graph data
Name 32S5-8,8,2-g5
Type Hyperbolic
Degree 32
Genus 5
Galois orbit size for 32S5-8,8,2-g5-path1 1
Galois orbit size for 32S5-8,8,2-g5-path10 1
Galois orbit size for 32S5-8,8,2-g5-path11 1
Galois orbit size for 32S5-8,8,2-g5-path12 1
Galois orbit size for 32S5-8,8,2-g5-path13 1
Galois orbit size for 32S5-8,8,2-g5-path14 1
Galois orbit size for 32S5-8,8,2-g5-path15 1
Galois orbit size for 32S5-8,8,2-g5-path16 1
Galois orbit size for 32S5-8,8,2-g5-path17 1
Galois orbit size for 32S5-8,8,2-g5-path18 1
Galois orbit size for 32S5-8,8,2-g5-path19 1
Galois orbit size for 32S5-8,8,2-g5-path2 1
Galois orbit size for 32S5-8,8,2-g5-path20 1
Galois orbit size for 32S5-8,8,2-g5-path21 1
Galois orbit size for 32S5-8,8,2-g5-path22 1
Galois orbit size for 32S5-8,8,2-g5-path23 1
Galois orbit size for 32S5-8,8,2-g5-path3 1
Galois orbit size for 32S5-8,8,2-g5-path4 1
Galois orbit size for 32S5-8,8,2-g5-path5 1
Galois orbit size for 32S5-8,8,2-g5-path6 1
Galois orbit size for 32S5-8,8,2-g5-path7 1
Galois orbit size for 32S5-8,8,2-g5-path8 1
Galois orbit size for 32S5-8,8,2-g5-path9 1
Passport size 1
Pointed size 1

Above

64S6-8,8,2-g9 64S29-16,16,2-g13 64S31-16,16,2-g13 64S4-8,8,2-g9 64S17-8,8,4-g17 64S29-16,16,4-g21 64S31-16,16,4-g21 64S30-16,16,4-g21 64S30-16,16,2-g13 64S5-8,8,4-g17 64S7-8,8,4-g17

Below

16T5-8,8,2-g3 16T10-4,4,2-g1 16T6-8,8,2-g3

Belyi Curve 1: 32S5-8,8,2-g5-path10

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

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

Belyi Curve 1 Degree: 16

Belyi Curve 1 Naive Measure: 17

Belyi Map 1 Numerator:

\(x_{4}^{8}\)

Belyi Map 1 Denominator:

\(x_{4}^{8} - 1\)

Belyi Curve 2: 32S5-8,8,2-g5-path11

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

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

Belyi Curve 2 Degree: 9

Belyi Curve 2 Naive Measure: 9

Belyi Map 2 Numerator:

\(-4\)

Belyi Map 2 Denominator:

\(x_{3}^{8} - 4\)

Belyi Curve 3: 32S5-8,8,2-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:

\(x_{3}^{8} - 4\)

Belyi Curve 4: 32S5-8,8,2-g5-path3

\(1/2(\nu^{3} + 5\nu )x_{1}x_{2}x_{3} - x_{1}x_{3} + x_{2}^{2}x_{4}^{2} - x_{4}^{2}\)
\(-x_{1}x_{3} + 1/2(\nu^{3} + 5\nu )x_{2}x_{4}^{2} + x_{3}^{2}x_{4}^{2}\)
\(x_{2}x_{3}^{2} - x_{2} + 1/2(\nu^{3} + 5\nu )x_{3}^{2} + 1/2(\nu^{3} + 5\nu )\)
\(x_{1}x_{4}^{2} + 1/2(\nu^{3} + 5\nu )x_{2}x_{3} - x_{3}3\)
\(x_{1}^{2} - x_{2}^{2} + 1\)

Belyi Curve 4 Base Field: \(\nu^{4}+6\nu^{2}+1\), discriminant [ <2, 14> ]

Belyi Curve 4 Degree: 16

Belyi Curve 4 Naive Measure: 37

Belyi Map 4 Numerator:

\(-1\)

Belyi Map 4 Denominator:

\(x_{4}^{8} - 1\)

Belyi Curve 5: 32S5-8,8,2-g5-path8

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

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

Belyi Curve 5 Degree: 10

Belyi Curve 5 Naive Measure: 11

Belyi Map 5 Numerator:

\(x_{2}^{8} + 4x_{2}^{6} + 6x_{2}^{4} + 4x_{2}^{2} + 1\)

Belyi Map 5 Denominator:

\(x_{2}^{8} - 12x_{2}^{6} + 38x_{2}^{4} - 12x_{2}^{2} + 1\)

Belyi Curve 6: 32S5-8,8,2-g5-path9

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

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

Belyi Curve 6 Degree: 10

Belyi Curve 6 Naive Measure: 11

Belyi Map 6 Numerator:

\(x_{2}^{8} + 4x_{2}^{6} + 6x_{2}^{4} + 4x_{2}^{2} + 1\)

Belyi Map 6 Denominator:

\(x_{2}^{8} - 12x_{2}^{6} + 38x_{2}^{4} - 12x_{2}^{2} + 1\)