Properties

Genus \(15\)
Quotient Genus \(0\)
Group \(C_3\times C_4:C_4\)
Signature \([ 0; 4, 12, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 15
Quotient Genus: 0
Group name: $C_3\times C_4:C_4$
Group identifier: [48,22]
Signature: $[ 0; 4, 12, 12 ]$
Conjugacy classes for this refined passport: 7, 23, 30

The full automorphism group for this family is $C_3:(D_4:C_4)$ with signature $[ 0; 2, 8, 12 ]$.

Jacobian variety group algebra decomposition:$E\times E\times E\times A_{2}\times A_{2}\times A_{2}^{2}\times A_{2}^{2}$
Corresponding character(s): 5, 6, 14, 18, 25, 27, 28

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

15.48-22.0.4-12-12.1.1

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