Properties

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: 3, 3, 3, 4, 5, 6

Jacobian variety group algebra decomposition:$E\times E\times E\times A_{2}$
Corresponding character(s): 2, 4, 6, 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.

5.8-5.0.2-2-2-2-2-2.44.1

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