16T12-8,4,2-g2

graph data
Name 16T12-8,4,2-g2
Type Hyperbolic
Degree 16
Genus 2
Galois orbit size for 16T12-8,4,2-g2-path1 1
Galois orbit size for 16T12-8,4,2-g2-path2 1
Galois orbit size for 16T12-8,4,2-g2-path3 1
Passport size 1
Pointed size 1

Above

32S13-8,4,4-g7 32S9-8,4,2-g3 32S10-8,4,4-g7

Below

8T4-4,2,2-g0

Belyi Curve 1: 16T12-8,4,2-g2-path1

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

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

Belyi Curve 1 Degree: 5

Belyi Curve 1 Naive Measure: 3

Belyi Map 1 Numerator:

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

Belyi Map 1 Denominator:

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

Belyi Curve 2: 16T12-8,4,2-g2-path2

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

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

Belyi Curve 2 Degree: 5

Belyi Curve 2 Naive Measure: 3

Belyi Map 2 Numerator:

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

Belyi Map 2 Denominator:

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

Belyi Curve 3: 16T12-8,4,2-g2-path3

\(-9/8x_{1}^{5}x_{3} - 9/8x_{1}x_{3}^{5} + x_{2}^{2}\)

Belyi Curve 3 Base Field: \(\nu^{4}+6\nu^{2}+1\), discriminant [ <2, 14> ]

Belyi Curve 3 Degree: 5

Belyi Curve 3 Naive Measure: 19

Belyi Map 3 Numerator:

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

Belyi Map 3 Denominator:

\(-3x_{1}^{4} + 8/9x_{1}^{3}x_{2}^{2} + 1\)