16T6-8,2,8-g3

graph data
Name 16T6-8,2,8-g3
Type Hyperbolic
Degree 16
Genus 3
Galois orbit size for 16T6-8,2,8-g3-path1 1
Galois orbit size for 16T6-8,2,8-g3-path2 1
Galois orbit size for 16T6-8,2,8-g3-path3 1
Galois orbit size for 16T6-8,2,8-g3-path4 1
Galois orbit size for 16T6-8,2,8-g3-path5 1
Passport size 1
Pointed size 1

Above

32S5-8,2,8-g5 32S12-8,4,8-g9 32S4-8,4,8-g9

Below

8T2-4,2,4-g1

Belyi Curve 1: 16T6-8,2,8-g3-path1

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

Belyi Curve 1 Base Field: Rationals

Belyi Curve 1 Degree: 8

Belyi Curve 1 Naive Measure: 6

Belyi Map 1 Numerator:

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

Belyi Map 1 Denominator:

\(16\)

Belyi Curve 2: 16T6-8,2,8-g3-path3

\(256/65535x_{1}^{8} + 8192/4294836225\nu x_{1}^{7}x_{3} + 114688/4294836225x_{1}^{6}x_{3}^{2} - 917504/4294836225\nu x_{1}^{5}x_{3}^{3} - 917504/858967245x_{1}^{4}x_{3}^{4} + 14680064/4294836225\nu x_{1}^{3}x_{3}^{5} + 29360128/4294836225x_{1}^{2}x_{3}^{6} - 33554432/4294836225\nu x_{1}x_{3}^{7} + x_{2}^{2} - 16777216/4294836225x_{3}^{8}\)

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

Belyi Curve 2 Degree: 8

Belyi Curve 2 Naive Measure: 30922886356

Belyi Map 2 Numerator:

\(-32/65535\nu x_{1}^{7} - 448/65535x_{1}^{6} + 3584/65535\nu x_{1}^{5} + 3584/13107x_{1}^{4} - 57344/65535\nu x_{1}^{3} - 114688/65535x_{1}^{2} + 131072/65535\nu x_{1} - 65535/16777216x_{2}^{2} + 65536/65535\)

Belyi Map 2 Denominator:

\(-32/65535\nu x_{1}^{7} - 448/65535x_{1}^{6} + 3584/65535\nu x_{1}^{5} + 3584/13107x_{1}^{4} - 57344/65535\nu x_{1}^{3} - 114688/65535x_{1}^{2} + 131072/65535\nu x_{1} - 65535/256x_{2}^{2} + 65536/65535\)

Belyi Curve 3: 16T6-8,2,8-g3-path4

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

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 8

Belyi Curve 3 Naive Measure: 3

Belyi Map 3 Numerator:

\(1\)

Belyi Map 3 Denominator:

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

Belyi Curve 4: 16T6-8,2,8-g3-path5

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

Belyi Curve 4 Base Field: Rationals

Belyi Curve 4 Degree: 8

Belyi Curve 4 Naive Measure: 3

Belyi Map 4 Numerator:

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

Belyi Map 4 Denominator:

\(4\)