Properties

Genus \(7\)
Quotient Genus \(0\)
Group \(C_8:C_4\)
Signature \([ 0; 4, 4, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 7
Quotient Genus: 0
Group name: $C_8:C_4$
Group identifier: [32,13]
Signature: $[ 0; 4, 4, 8 ]$
Conjugacy classes for this refined passport: 7, 9, 13

The full automorphism group for this family is $OD_{32}:C_2$ with signature $[ 0; 2, 4, 16 ]$.

Jacobian variety group algebra decomposition:$E\times A_{2}\times E^{2}\times E^{2}$
Corresponding character(s): 5, 10, 11, 12

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

7.32-13.0.4-4-8.1.1

  (1,17,3,19) (2,18,4,20) (5,22,7,24) (6,21,8,23) (9,29,11,31) (10,30,12,32) (13,25,15,27) (14,26,16,28)
  (1,26,4,27) (2,25,3,28) (5,29,8,32) (6,30,7,31) (9,17,12,20) (10,18,11,19) (13,22,16,23) (14,21,15,24)
  (1,15,6,11,2,16,5,12) (3,13,8,9,4,14,7,10) (17,31,22,27,18,32,21,28) (19,29,24,25,20,30,23,26)