Properties

Genus \(3\)
Quotient Genus \(0\)
Group \(D_4\)
Signature \([ 0; 2, 2, 4, 4 ]\)
Generating Vectors \(2\)

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Family Information

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

The full automorphism group for this family is $C_2\times D_4$ with signature $[ 0; 2, 2, 2, 4 ]$.

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

Generating Vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

3.8-3.0.2-2-4-4.1.1

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

3.8-3.0.2-2-4-4.1.2
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,7,2,8) (3,6,4,5)
  (1,7,2,8) (3,6,4,5)

Display number of generating vectors: