32S20-4,16,4-g8

graph data
Name 32S20-4,16,4-g8
Type Hyperbolic
Degree 32
Genus 8
Galois orbit size for 32S20-4,16,4-g8-path1 1
Galois orbit size for 32S20-4,16,4-g8-path2 1
Galois orbit size for 32S20-4,16,4-g8-path3 1
Passport size 1
Pointed size 1

Above

64S47-4,16,4-g15 64S39-4,16,4-g15

Below

16T13-2,8,2-g0

Belyi Curve 1: 32S20-4,16,4-g8-path1

\(-x_{1}^{17}x_{3} + x_{1}x_{3}^{17} + x_{2}^{2}\)

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

Belyi Curve 1 Degree: 17

Belyi Curve 1 Naive Measure: 3

Belyi Map 1 Numerator:

\(x_{1}^{16} + 2x_{1}^{8} + 1\)

Belyi Map 1 Denominator:

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

Belyi Curve 2: 32S20-4,16,4-g8-path2

\(x_{1}^{17}x_{3} - x_{1}x_{3}^{17} + x_{2}^{2}\)

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 17

Belyi Curve 2 Naive Measure: 3

Belyi Map 2 Numerator:

\(x_{1}^{16} + 2x_{1}^{8} + 1\)

Belyi Map 2 Denominator:

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

Belyi Curve 3: 32S20-4,16,4-g8-path3

\(-x_{1}^{17}x_{3} + x_{1}x_{3}^{17} + x_{2}^{2}\)

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

Belyi Curve 3 Degree: 17

Belyi Curve 3 Naive Measure: 3

Belyi Map 3 Numerator:

\(x_{1}^{16} + 2x_{1}^{8} + 1\)

Belyi Map 3 Denominator:

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