16T6-8,8,2-g3

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

Above

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

Below

8T2-4,4,2-g1

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

\(-16\)

Belyi Map 1 Denominator:

\(x_{1}^{8} - 16\)

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

\(4/4095x_{1}^{8} + 65536/16769025x_{1}^{7}x_{3} + 16384/2395575x_{1}^{6}x_{3}^{2} + 16384/2395575x_{1}^{5}x_{3}^{3} + 2048/479115x_{1}^{4}x_{3}^{4} + 4096/2395575x_{1}^{3}x_{3}^{5} + 1024/2395575x_{1}^{2}x_{3}^{6} + 1024/16769025x_{1}x_{3}^{7} + x_{2}^{2} + 64/16769025x_{3}^{8}\)

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

Belyi Curve 2 Degree: 8

Belyi Curve 2 Naive Measure: 60372586

Belyi Map 2 Numerator:

\(16384/16769025x_{1}^{7} + 4096/2395575x_{1}^{6} + 4096/2395575x_{1}^{5} + 512/479115x_{1}^{4} + 1024/2395575x_{1}^{3} + 256/2395575x_{1}^{2} + 256/16769025x_{1} + 1/4x_{2}^{2} + 16/16769025\)

Belyi Map 2 Denominator:

\(-4095/4x_{2}^{2}\)

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

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

Belyi Map 3 Denominator:

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

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

\(-x_{1}^{7}x_{3} - 7x_{1}^{5}x_{3}^{3} - 7x_{1}^{3}x_{3}^{5} - x_{1}x_{3}^{7} + x_{2}^{2}\)

Belyi Curve 4 Base Field: Rationals

Belyi Curve 4 Degree: 7

Belyi Curve 4 Naive Measure: 17

Belyi Map 4 Numerator:

\(-21x_{1}^{6} - 63x_{1}^{4} - 27x_{1}^{2} - x_{1}x_{2}^{2} + 8x_{2}^{2} - 1\)

Belyi Map 4 Denominator:

\(16x_{2}^{2}\)