32S17-8,16,16-g13

graph data
Name 32S17-8,16,16-g13
Type Hyperbolic
Degree 32
Genus 13
Galois orbit size for 32S17-8,16,16-g13-path1 1
Galois orbit size for 32S17-8,16,16-g13-path10 1
Galois orbit size for 32S17-8,16,16-g13-path11 1
Galois orbit size for 32S17-8,16,16-g13-path12 1
Galois orbit size for 32S17-8,16,16-g13-path13 1
Galois orbit size for 32S17-8,16,16-g13-path14 1
Galois orbit size for 32S17-8,16,16-g13-path2 1
Galois orbit size for 32S17-8,16,16-g13-path3 1
Galois orbit size for 32S17-8,16,16-g13-path4 1
Galois orbit size for 32S17-8,16,16-g13-path5 1
Galois orbit size for 32S17-8,16,16-g13-path6 1
Galois orbit size for 32S17-8,16,16-g13-path7 1
Galois orbit size for 32S17-8,16,16-g13-path8 1
Galois orbit size for 32S17-8,16,16-g13-path9 1
Passport size 2
Pointed size 2

Above

64S44-8,16,16-g25 64S29-8,16,16-g25 64S27-8,16,16-g25

Below

16T5-4,8,8-g5

Belyi Curve 1: 32S17-8,16,16-g13-path10

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

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

Belyi Curve 1 Degree: 20

Belyi Curve 1 Naive Measure: 11

Belyi Map 1 Numerator:

\(x_{3}^{2}x_{5}^{8}\)

Belyi Map 1 Denominator:

\(1\)

Belyi Curve 2: 32S17-8,16,16-g13-path11

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

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 24

Belyi Curve 2 Naive Measure: 16

Belyi Map 2 Numerator:

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

Belyi Map 2 Denominator:

\(1\)

Belyi Curve 3: 32S17-8,16,16-g13-path12

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

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 24

Belyi Curve 3 Naive Measure: 16

Belyi Map 3 Numerator:

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

Belyi Map 3 Denominator:

\(1\)

Belyi Curve 4: 32S17-8,16,16-g13-path13

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

Belyi Curve 4 Base Field: Rationals

Belyi Curve 4 Degree: 20

Belyi Curve 4 Naive Measure: 36

Belyi Map 4 Numerator:

\(-1/4096x_{3}^{4}x_{4}^{24} - 5/128x_{3}^{4}x_{4}^{16} - 9/8x_{3}^{4}x_{4}^{8} + 1/4096x_{3}^{3}x_{4}^{26} + 19/512x_{3}^{3}x_{4}^{18} + 15/16x_{3}^{3}x_{4}^{10} - 1/2x_{3}^{3}x_{4}^{2} - 1/8192x_{3}^{2}x_{4}^{28} - 19/1024x_{3}^{2}x_{4}^{20} - 31/64x_{3}^{2}x_{4}^{12} - 1/4x_{3}^{2}x_{4}^{4} + 1/32x_{3}x_{4}^{14} + 2x_{3}x_{4}^{6} - 1/1024x_{4}^{24} - 9/64x_{4}^{16} - 13/4x_{4}^{8}\)

Belyi Map 4 Denominator:

\(8x_{2} + 1/4x_{3}^{4}x_{4}^{8} - 1/4x_{3}^{3}x_{4}^{10} + 2x_{3}^{3}x_{4}^{2} + 1/8x_{3}^{2}x_{4}^{12} - x_{3}^{2}x_{4}^{4} + x_{4}^{8} - 4\)

Belyi Curve 5: 32S17-8,16,16-g13-path14

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

Belyi Curve 5 Base Field: Rationals

Belyi Curve 5 Degree: 20

Belyi Curve 5 Naive Measure: 36

Belyi Map 5 Numerator:

\(-x_{3}^{16} - 10x_{3}^{8} + x_{3}^{4}x_{4}^{24} + 266x_{3}^{4}x_{4}^{16} + 210x_{3}^{4}x_{4}^{8} - 130x_{3}^{3}x_{4}^{26} - 851x_{3}^{3}x_{4}^{18} - 398x_{3}^{3}x_{4}^{10} + 9x_{3}^{3}x_{4}^{2} + 130x_{3}^{2}x_{4}^{28} + 467x_{3}^{2}x_{4}^{20} + 15x_{3}^{2}x_{4}^{12} + 9x_{3}^{2}x_{4}^{4} - 516x_{3}x_{4}^{14} - 272x_{3}x_{4}^{6} + 260x_{4}^{24} + 1060x_{4}^{16} + 404x_{4}^{8}\)

Belyi Map 5 Denominator:

\(8x_{2} + 4x_{3}^{8} - 4x_{3}^{4}x_{4}^{8} - 8x_{3}^{4} + 40x_{3}^{3}x_{4}^{10} + 28x_{3}^{3}x_{4}^{2} - 40x_{3}^{2}x_{4}^{12} + 4x_{3}^{2}x_{4}^{4} - 80x_{4}^{8} - 4\)

Belyi Curve 6: 32S17-8,16,16-g13-path5

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

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

Belyi Curve 6 Degree: 18

Belyi Curve 6 Naive Measure: 11

Belyi Map 6 Numerator:

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

Belyi Map 6 Denominator:

\(1\)

Belyi Curve 7: 32S17-8,16,16-g13-path9

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

Belyi Curve 7 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 7 Degree: 24

Belyi Curve 7 Naive Measure: 16

Belyi Map 7 Numerator:

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

Belyi Map 7 Denominator:

\(1\)