Properties

Label 6.8-1.0.2-2-2-8-8.1
Genus \(6\)
Quotient genus \(0\)
Group \(C_8\)
Signature \([ 0; 2, 2, 2, 8, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $6$
Quotient genus: $0$
Group name: $C_8$
Group identifier: $[8,1]$
Signature: $[ 0; 2, 2, 2, 8, 8 ]$
Conjugacy classes for this refined passport: $2, 2, 2, 5, 6$

Jacobian variety group algebra decomposition:$A_{6}$
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:
  $y^2=x(x^{12}+a_{1}x^{8}+a_{2}x^{4}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

6.8-1.0.2-2-2-8-8.1.1

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