Properties

Label 7.12-1.0.4-4-4-4.3
Genus \(7\)
Quotient genus \(0\)
Group \(C_3:C_4\)
Signature \([ 0; 4, 4, 4, 4 ]\)
Generating Vectors \(4\)

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Family Information

Genus: $7$
Quotient genus: $0$
Group name: $C_3:C_4$
Group identifier: $[12,1]$
Signature: $[ 0; 4, 4, 4, 4 ]$
Conjugacy classes for this refined passport: $5, 5, 5, 5$

The full automorphism group for this family is $S_3\times D_4$ with signature $[ 0; 2, 2, 2, 4 ]$.

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

Generating vector(s)

Displaying 4 of 4 generating vectors for this refined passport.

7.12-1.0.4-4-4-4.3.1

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

7.12-1.0.4-4-4-4.3.2
  (1,10,4,7) (2,12,5,9) (3,11,6,8)
  (1,12,4,9) (2,11,5,8) (3,10,6,7)
  (1,10,4,7) (2,12,5,9) (3,11,6,8)
  (1,11,4,8) (2,10,5,7) (3,12,6,9)

7.12-1.0.4-4-4-4.3.3
  (1,10,4,7) (2,12,5,9) (3,11,6,8)
  (1,12,4,9) (2,11,5,8) (3,10,6,7)
  (1,12,4,9) (2,11,5,8) (3,10,6,7)
  (1,10,4,7) (2,12,5,9) (3,11,6,8)

7.12-1.0.4-4-4-4.3.4
  (1,10,4,7) (2,12,5,9) (3,11,6,8)
  (1,12,4,9) (2,11,5,8) (3,10,6,7)
  (1,11,4,8) (2,10,5,7) (3,12,6,9)
  (1,12,4,9) (2,11,5,8) (3,10,6,7)

Display number of generating vectors:

Displaying the unique representative of this refined passport up to braid equivalence.

  7.12-1.0.4-4-4-4.3.1

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