16T14-4,8,4-g4

graph data
Name 16T14-4,8,4-g4
Type Hyperbolic
Degree 16
Genus 4
Galois orbit size for 16T14-4,8,4-g4-path1 1
Galois orbit size for 16T14-4,8,4-g4-path2 1
Galois orbit size for 16T14-4,8,4-g4-path3 1
Passport size 1
Pointed size 1

Above

32S10-4,8,4-g7 32S14-4,8,4-g7

Below

8T4-2,4,2-g0

Belyi Curve 1: 16T14-4,8,4-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:

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

Belyi Map 1 Denominator:

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

Belyi Curve 2: 16T14-4,8,4-g4-path2

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

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 9

Belyi Curve 2 Naive Measure: 3

Belyi Map 2 Numerator:

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

Belyi Map 2 Denominator:

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

Belyi Curve 3: 16T14-4,8,4-g4-path3

\(-25x_{1}^{9}x_{3} + 75/2x_{1}^{7}x_{3}^{3} - 75/32x_{1}^{3}x_{3}^{7} + 25/256x_{1}x_{3}^{9} + x_{2}^{2}\)

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

Belyi Curve 3 Degree: 9

Belyi Curve 3 Naive Measure: 432

Belyi Map 3 Numerator:

\(-1/4x_{1}^{8} + 3/4x_{1}^{6} - 19/32x_{1}^{4} + 3/64x_{1}^{2} - 1/1024\)

Belyi Map 3 Denominator:

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