Properties

Label 5.8-5.0.2-2-2-2-2-2.21
Genus \(5\)
Quotient genus \(0\)
Group \(C_2^3\)
Signature \([ 0; 2, 2, 2, 2, 2, 2 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $5$
Quotient genus: $0$
Group name: $C_2^3$
Group identifier: $[8,5]$
Signature: $[ 0; 2, 2, 2, 2, 2, 2 ]$
Conjugacy classes for this refined passport: $2, 3, 3, 3, 6, 7$

Jacobian variety group algebra decomposition:$E\times E\times E\times A_{2}$
Corresponding character(s): $3, 4, 7, 8$

Other Data

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

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

5.8-5.0.2-2-2-2-2-2.21.1

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