32S16-16,16,2-g7

graph data
Name 32S16-16,16,2-g7
Type Hyperbolic
Degree 32
Genus 7
Galois orbit size for 32S16-16,16,2-g7-path1 1
Galois orbit size for 32S16-16,16,2-g7-path2 1
Galois orbit size for 32S16-16,16,2-g7-path3 1
Galois orbit size for 32S16-16,16,2-g7-path4 1
Galois orbit size for 32S16-16,16,2-g7-path5 1
Galois orbit size for 32S16-16,16,2-g7-path6 1
Galois orbit size for 32S16-16,16,2-g7-path7 1
Galois orbit size for 32S16-16,16,2-g7-path8 1
Galois orbit size for 32S16-16,16,2-g7-path9 1
Passport size 1
Pointed size 1

Above

64S50-32,32,4-g23 64S51-32,32,4-g23 64S44-16,16,4-g21 64S51-32,32,2-g15 64S26-16,16,4-g21 64S50-32,32,2-g15 64S29-16,16,2-g13

Below

16T1-16,16,1-g0 16T1-16,16,2-g4 16T5-8,8,2-g3

Belyi Curve 1: 32S16-16,16,2-g7-path1

\(-x_{1}^{16} + x_{2}^{2} + x_{3}^{16}\)

Belyi Curve 1 Base Field: Rationals

Belyi Curve 1 Degree: 16

Belyi Curve 1 Naive Measure: 3

Belyi Map 1 Numerator:

\(-1\)

Belyi Map 1 Denominator:

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

Belyi Curve 2: 32S16-16,16,2-g7-path3

\(x_{1}^{16} + x_{2}^{2} - x_{3}^{16}\)

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 16

Belyi Curve 2 Naive Measure: 3

Belyi Map 2 Numerator:

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

Belyi Map 2 Denominator:

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

Belyi Curve 3: 32S16-16,16,2-g7-path5

\(x_{1}^{8}x_{2} + x_{2}^{2} + 4x_{3}^{16}\)

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 16

Belyi Curve 3 Naive Measure: 6

Belyi Map 3 Numerator:

\(-16\)

Belyi Map 3 Denominator:

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

Belyi Curve 4: 32S16-16,16,2-g7-path7

\(-894348/13981x_{1}^{16} + 19079424/4886709025\nu x_{1}^{15}x_{3} - 114476544/977341805x_{1}^{14}x_{3}^{2} - 2136895488/977341805\nu x_{1}^{13}x_{3}^{3} + 27779641344/977341805x_{1}^{12}x_{3}^{4} + 1333422784512/4886709025\nu x_{1}^{11}x_{3}^{5} - 888948523008/444246275x_{1}^{10}x_{3}^{6} - 1015941169152/88849255\nu x_{1}^{9}x_{3}^{7} + 4571735261184/88849255x_{1}^{8}x_{3}^{8} + 16255058706432/88849255\nu x_{1}^{7}x_{3}^{9} - 227570821890048/444246275x_{1}^{6}x_{3}^{10} - 5461699725361152/4886709025\nu x_{1}^{5}x_{3}^{11} + 1820566575120384/977341805x_{1}^{4}x_{3}^{12} + 2240697323225088/977341805\nu x_{1}^{3}x_{3}^{13} - 1920597705621504/977341805x_{1}^{2}x_{3}^{14} - 5121593881657344/4886709025\nu x_{1}x_{3}^{15} + x_{2}^{2} + 1280398470414336/4886709025x_{3}^{16}\)

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

Belyi Curve 4 Degree: 16

Belyi Curve 4 Naive Measure: 18097225391216155

Belyi Map 4 Numerator:

\(67108864/1099509530625\nu x_{1}^{15} - 134217728/73300635375x_{1}^{14} - 7516192768/219901906125\nu x_{1}^{13} + 97710505984/219901906125x_{1}^{12} + 1563368095744/366503176875\nu x_{1}^{11} - 3126736191488/99955411875x_{1}^{10} - 3573412790272/19991082375\nu x_{1}^{9} + 1786706395136/2221231375x_{1}^{8} + 57174604644352/19991082375\nu x_{1}^{7} - 800444465020928/99955411875x_{1}^{6} - 6403555720167424/366503176875\nu x_{1}^{5} + 6403555720167424/219901906125x_{1}^{4} + 7881299347898368/219901906125\nu x_{1}^{3} - 2251799813685248/73300635375x_{1}^{2} - 18014398509481984/1099509530625\nu x_{1} + 262144/16769025x_{2}^{2} + 4503599627370496/1099509530625\)

Belyi Map 4 Denominator:

\(13981/894348x_{2}^{2}\)

Belyi Curve 5: 32S16-16,16,2-g7-path8

\(x_{1}^{8}x_{2} + x_{2}^{2} + 4x_{3}^{16}\)

Belyi Curve 5 Base Field: Rationals

Belyi Curve 5 Degree: 16

Belyi Curve 5 Naive Measure: 6

Belyi Map 5 Numerator:

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

Belyi Map 5 Denominator:

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

Belyi Curve 6: 32S16-16,16,2-g7-path9

\(x_{1}^{16} + x_{2}^{2} - x_{3}^{16}\)

Belyi Curve 6 Base Field: Rationals

Belyi Curve 6 Degree: 16

Belyi Curve 6 Naive Measure: 3

Belyi Map 6 Numerator:

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

Belyi Map 6 Denominator:

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