Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(C_8\)
Signature \([ 0; 2, 2, 2, 2, 2, 8, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_8$
Group identifier: [8,1]
Signature: $[ 0; 2, 2, 2, 2, 2, 8, 8 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 2, 2, 7, 8

Jacobian variety group algebra decomposition:$A_{10}$
Corresponding character(s): 2

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,2) (3,4) (5,6) (7,8)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{20}+a_{1}x^{16}+a_{2}x^{12}+a_{3}x^{8}+a_{4}x^{4}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.8-1.0.2-2-2-2-2-8-8.2.1

  (1,2) (3,4) (5,6) (7,8)
  (1,2) (3,4) (5,6) (7,8)
  (1,2) (3,4) (5,6) (7,8)
  (1,2) (3,4) (5,6) (7,8)
  (1,2) (3,4) (5,6) (7,8)
  (1,6,3,8,2,5,4,7)
  (1,8,4,6,2,7,3,5)