32S19-16,2,4-g4

graph data
Name 32S19-16,2,4-g4
Type Hyperbolic
Degree 32
Genus 4
Galois orbit size for 32S19-16,2,4-g4-path1 1
Galois orbit size for 32S19-16,2,4-g4-path2 1
Galois orbit size for 32S19-16,2,4-g4-path3 1
Passport size 1
Pointed size 1

Above

64S38-16,2,4-g7 64S39-16,4,4-g15 64S48-16,4,4-g15

Below

16T13-8,2,2-g0

Belyi Curve 1: 32S19-16,2,4-g4-path1

\(-x_{1}^{9}x_{3} + x_{1}x_{3}^{9} + x_{2}^{2}\)

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

Belyi Curve 1 Degree: 9

Belyi Curve 1 Naive Measure: 3

Belyi Map 1 Numerator:

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

Belyi Map 1 Denominator:

\(-x_{1}^{8} + x_{1}^{7}x_{2}^{2} + 1\)

Belyi Curve 2: 32S19-16,2,4-g4-path2

\(-x_{1}^{9}x_{3} + x_{1}x_{3}^{9} + x_{2}^{2}\)

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

Belyi Curve 2 Degree: 9

Belyi Curve 2 Naive Measure: 3

Belyi Map 2 Numerator:

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

Belyi Map 2 Denominator:

\(-x_{1}^{8} + x_{1}^{7}x_{2}^{2} + 1\)

Belyi Curve 3: 32S19-16,2,4-g4-path3

\(x_{1}^{9}x_{3} - x_{1}x_{3}^{9} + x_{2}^{2}\)

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 9

Belyi Curve 3 Naive Measure: 3

Belyi Map 3 Numerator:

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

Belyi Map 3 Denominator:

\(-x_{1}^{8} - x_{1}^{7}x_{2}^{2} + 1\)