Properties

Label 8.8-1.0.2-2-2-2-8-8.1
Genus \(8\)
Quotient genus \(0\)
Group \(C_8\)
Signature \([ 0; 2, 2, 2, 2, 8, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $8$
Quotient genus: $0$
Group name: $C_8$
Group identifier: $[8,1]$
Signature: $[ 0; 2, 2, 2, 2, 8, 8 ]$
Conjugacy classes for this refined passport: $2, 2, 2, 2, 5, 8$

Jacobian variety group algebra decomposition:$A_{8}$

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:
  $y^2=x(x^{16}+a_{1}x^{12}+a_{2}x^{8}+a_{3}x^{4}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

8.8-1.0.2-2-2-2-8-8.1.1

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