Properties

Label 8.12-1.0.4-4-6-6.1
Genus \(8\)
Quotient genus \(0\)
Group \(C_3:C_4\)
Signature \([ 0; 4, 4, 6, 6 ]\)
Generating Vectors \(2\)

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Family Information

Genus: $8$
Quotient genus: $0$
Group name: $C_3:C_4$
Group identifier: $[12,1]$
Signature: $[ 0; 4, 4, 6, 6 ]$
Conjugacy classes for this refined passport: $4, 5, 6, 6$

The full automorphism group for this family is $C_3:D_4$ with signature $[ 0; 2, 2, 4, 6 ]$.

Jacobian variety group algebra decomposition:$A_{2}\times A_{4}\times E^{2}$
Corresponding character(s): $3, 5, 6$

Generating vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

8.12-1.0.4-4-6-6.1.1

  (1,7,4,10) (2,9,5,12) (3,8,6,11)
  (1,10,4,7) (2,12,5,9) (3,11,6,8)
  (1,5,3,4,2,6) (7,11,9,10,8,12)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

8.12-1.0.4-4-6-6.1.2
  (1,7,4,10) (2,9,5,12) (3,8,6,11)
  (1,12,4,9) (2,11,5,8) (3,10,6,7)
  (1,6,2,4,3,5) (7,12,8,10,9,11)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

Display number of generating vectors: