Properties

Genus \(3\)
Quotient Genus \(1\)
Group \(D_4\)
Signature \([ 1; 2 ]\)
Generating Vectors \(24\)

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Family Information

Genus: 3
Quotient Genus: 1
Group name: $D_4$
Group identifier: [8,3]
Signature: $[ 1; 2 ]$
Conjugacy classes for this refined passport: 2

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): 1, 5

Generating Vector(s)

Displaying 20 of 24 generating vectors for this refined passport.

3.8-3.1.2.1.1

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

3.8-3.1.2.1.2
  (1,6) (2,5) (3,7) (4,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.3
  (1,8,2,7) (3,5,4,6)
  (1,3) (2,4) (5,7) (6,8)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.4
  (1,7,2,8) (3,6,4,5)
  (1,3) (2,4) (5,7) (6,8)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.5
  (1,3) (2,4) (5,7) (6,8)
  (1,5) (2,6) (3,8) (4,7)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.6
  (1,4) (2,3) (5,8) (6,7)
  (1,5) (2,6) (3,8) (4,7)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.7
  (1,8,2,7) (3,5,4,6)
  (1,5) (2,6) (3,8) (4,7)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.8
  (1,7,2,8) (3,6,4,5)
  (1,5) (2,6) (3,8) (4,7)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.9
  (1,5) (2,6) (3,8) (4,7)
  (1,4) (2,3) (5,8) (6,7)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.10
  (1,6) (2,5) (3,7) (4,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.11
  (1,8,2,7) (3,5,4,6)
  (1,4) (2,3) (5,8) (6,7)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.12
  (1,7,2,8) (3,6,4,5)
  (1,4) (2,3) (5,8) (6,7)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.13
  (1,3) (2,4) (5,7) (6,8)
  (1,6) (2,5) (3,7) (4,8)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.14
  (1,4) (2,3) (5,8) (6,7)
  (1,6) (2,5) (3,7) (4,8)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.15
  (1,8,2,7) (3,5,4,6)
  (1,6) (2,5) (3,7) (4,8)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.16
  (1,7,2,8) (3,6,4,5)
  (1,6) (2,5) (3,7) (4,8)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.17
  (1,3) (2,4) (5,7) (6,8)
  (1,8,2,7) (3,5,4,6)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.18
  (1,5) (2,6) (3,8) (4,7)
  (1,8,2,7) (3,5,4,6)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.19
  (1,4) (2,3) (5,8) (6,7)
  (1,8,2,7) (3,5,4,6)
  (1,2) (3,4) (5,6) (7,8)

3.8-3.1.2.1.20
  (1,6) (2,5) (3,7) (4,8)
  (1,8,2,7) (3,5,4,6)
  (1,2) (3,4) (5,6) (7,8)

Display number of generating vectors: