Properties

Genus \(2\)
Quotient Genus \(0\)
Group \(D_4\)
Signature \([ 0; 2, 2, 2, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 2
Quotient Genus: 0
Group name: $D_4$
Group identifier: [8,3]
Signature: $[ 0; 2, 2, 2, 4 ]$
Conjugacy classes for this refined passport: 2, 3, 4, 5

Jacobian variety group algebra decomposition:$E^{2}$
Corresponding character(s): 5

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:
  $y^2=x(x^{4}+a_{1}x^{2}+1)$
  $y^2=(x^{2}-1)(x^{4}+a_{1}x^{2}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

2.8-3.0.2-2-2-4.1.1

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