Properties

Genus \(5\)
Quotient Genus \(0\)
Group \(Q_8\)
Signature \([ 0; 4, 4, 4, 4 ]\)
Generating Vectors \(2\)

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Family Information

Genus: 5
Quotient Genus: 0
Group name: $Q_8$
Group identifier: [8,4]
Signature: $[ 0; 4, 4, 4, 4 ]$
Conjugacy classes for this refined passport: 3, 3, 5, 5

The full automorphism group for this family is $C_8:C_2^2$ with signature $[ 0; 2, 2, 2, 4 ]$.

Jacobian variety group algebra decomposition:$E\times A_{4}$
Corresponding character(s): 4, 5

Generating Vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

5.8-4.0.4-4-4-4.2.1

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

5.8-4.0.4-4-4-4.2.2
  (1,3,2,4) (5,7,6,8)
  (1,4,2,3) (5,8,6,7)
  (1,7,2,8) (3,5,4,6)
  (1,8,2,7) (3,6,4,5)

Display number of generating vectors: