32S5-8,2,8-g5

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

Above

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

Below

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

Belyi Curve 1: 32S5-8,2,8-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: 32S5-8,2,8-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: 32S5-8,2,8-g5-path2

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

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

Belyi Curve 3 Degree: 10

Belyi Curve 3 Naive Measure: 11

Belyi Map 3 Numerator:

\(-16x_{2}^{6} - 32x_{2}^{4} - 16x_{2}^{2}\)

Belyi Map 3 Denominator:

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

Belyi Curve 4: 32S5-8,2,8-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: 32S5-8,2,8-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: 32S5-8,2,8-g5-path9

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

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

Belyi Curve 6 Degree: 10

Belyi Curve 6 Naive Measure: 19

Belyi Map 6 Numerator:

\(1/16x_{2}^{8} + 1/4x_{2}^{6} + 3/8x_{2}^{4} + 1/4x_{2}^{2} + 1/16\)

Belyi Map 6 Denominator:

\(x_{2}^{6} - 2x_{2}^{4} + x_{2}^{2}\)