32S1-32,32,8-g14

graph data
Name 32S1-32,32,8-g14
Type Hyperbolic
Degree 32
Genus 14
Galois orbit size for 32S1-32,32,8-g14-path1 2
Galois orbit size for 32S1-32,32,8-g14-path2 2
Passport size 4
Pointed size 4

Above

64S50-32,32,8-g27 64S1-64,64,16-g30

Below

16T1-16,16,4-g6

Belyi Curve 1: 32S1-32,32,8-g14-path1

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

Belyi Curve 1 Base Field: Rationals

Belyi Curve 1 Degree: 26

Belyi Curve 1 Naive Measure: 11

Belyi Map 1 Numerator:

\(-x_{2}^{2}x_{4}^{36} - x_{2}^{2}x_{4}^{20} - 3x_{2}x_{4}^{32} - 4x_{2}x_{4}^{16} + x_{2} - 2x_{4}^{28} - 2x_{4}^{12}\)

Belyi Map 1 Denominator:

\(8x_{4}^{12}\)

Belyi Curve 2: 32S1-32,32,8-g14-path2

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

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 26

Belyi Curve 2 Naive Measure: 11

Belyi Map 2 Numerator:

\(-x_{2}^{2}x_{4}^{36} - x_{2}^{2}x_{4}^{20} - 3x_{2}x_{4}^{32} - 4x_{2}x_{4}^{16} + x_{2} - 2x_{4}^{28} - 2x_{4}^{12}\)

Belyi Map 2 Denominator:

\(8x_{4}^{12}\)