Properties

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

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Family Information

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

Jacobian variety group algebra decomposition:$E\times E\times E^{2}$
Corresponding character(s): 2, 4, 5

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):No

Generating Vector(s)

Displaying 4 of 4 generating vectors for this refined passport.

4.8-3.0.2-2-2-2-4.2.1

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

4.8-3.0.2-2-2-2-4.2.2
  (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) (3,8) (4,7)
  (1,8,2,7) (3,5,4,6)

4.8-3.0.2-2-2-2-4.2.3
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,3) (2,4) (5,7) (6,8)
  (1,5) (2,6) (3,8) (4,7)
  (1,8,2,7) (3,5,4,6)

4.8-3.0.2-2-2-2-4.2.4
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,4) (2,3) (5,8) (6,7)
  (1,5) (2,6) (3,8) (4,7)
  (1,7,2,8) (3,6,4,5)

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