Properties

Genus \(13\)
Quotient genus \(0\)
Group \(C_{13}:C_4\)
Signature \([ 0; 4, 4, 26 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 13
Quotient genus: 0
Group name: $C_{13}:C_4$
Group identifier: [52,1]
Signature: $[ 0; 4, 4, 26 ]$
Conjugacy classes for this refined passport: 4, 4, 11

The full automorphism group for this family is $C_4\times D_{13}$ with signature $[ 0; 2, 4, 52 ]$.

Jacobian variety group algebra decomposition:$E\times A_{12}$
Corresponding character(s): 3, 5

Generating vector(s)

Displaying the unique generating vector for this refined passport.

13.52-1.0.4-4-26.7.1

  (1,40,14,27) (2,52,15,39) (3,51,16,38) (4,50,17,37) (5,49,18,36) (6,48,19,35) (7,47,20,34) (8,46,21,33) (9,45,22,32) (10,44,23,31) (11,43,24,30) (12,42,25,29) (13,41,26,28)
  (1,52,14,39) (2,51,15,38) (3,50,16,37) (4,49,17,36) (5,48,18,35) (6,47,19,34) (7,46,20,33) (8,45,21,32) (9,44,22,31) (10,43,23,30) (11,42,24,29) (12,41,25,28) (13,40,26,27)
  (1,15,3,17,5,19,7,21,9,23,11,25,13,14,2,16,4,18,6,20,8,22,10,24,12,26) (27,41,29,43,31,45,33,47,35,49,37,51,39,40,28,42,30,44,32,46,34,48,36,50,38,52)