16T6-4,8,8-g5

graph data
Name 16T6-4,8,8-g5
Type Hyperbolic
Degree 16
Genus 5
Galois orbit size for 16T6-4,8,8-g5-path1 1
Galois orbit size for 16T6-4,8,8-g5-path2 1
Galois orbit size for 16T6-4,8,8-g5-path3 1
Galois orbit size for 16T6-4,8,8-g5-path4 1
Galois orbit size for 16T6-4,8,8-g5-path5 1
Passport size 1
Pointed size 1

Above

32S5-4,8,8-g9 32S12-4,8,8-g9 32S4-4,8,8-g9

Below

8T2-2,4,4-g1

Belyi Curve 1: 16T6-4,8,8-g5-path1

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

Belyi Curve 1 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 1 Degree: 10

Belyi Curve 1 Naive Measure: 11

Belyi Map 1 Numerator:

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

Belyi Map 1 Denominator:

\(x_{2}^{2}\)

Belyi Curve 2: 16T6-4,8,8-g5-path3

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

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

Belyi Curve 2 Degree: 10

Belyi Curve 2 Naive Measure: 9

Belyi Map 2 Numerator:

\(x_{3}^{2}x_{4}^{4}\)

Belyi Map 2 Denominator:

\(1\)

Belyi Curve 3: 16T6-4,8,8-g5-path4

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

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 10

Belyi Curve 3 Naive Measure: 12

Belyi Map 3 Numerator:

\(x_{3}^{2}x_{4}^{4}\)

Belyi Map 3 Denominator:

\(1\)

Belyi Curve 4: 16T6-4,8,8-g5-path5

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

Belyi Curve 4 Base Field: Rationals

Belyi Curve 4 Degree: 9

Belyi Curve 4 Naive Measure: 6

Belyi Map 4 Numerator:

\(x_{2}^{3}x_{3}^{4} - x_{2}^{2}x_{3}^{8} - 3x_{2}x_{3}^{4} - x_{3}^{8}\)

Belyi Map 4 Denominator:

\(4\)