Properties

Genus \(13\)
Quotient Genus \(0\)
Group \(C_2\times C_3:S_3.C_2\)
Signature \([ 0; 4, 4, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 13
Quotient Genus: 0
Group name: $C_2\times C_3:S_3.C_2$
Group identifier: [72,45]
Signature: $[ 0; 4, 4, 6 ]$
Conjugacy classes for this refined passport: 7, 10, 11

The full automorphism group for this family is $S_3^2:C_4$ with signature $[ 0; 2, 4, 12 ]$.

Jacobian variety group algebra decomposition:$E\times E^{4}\times E^{4}\times E^{4}$
Corresponding character(s): 7, 9, 10, 12

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

13.72-45.0.4-4-6.1.1

  (1,37,10,46) (2,45,12,50) (3,41,11,54) (4,42,16,53) (5,38,18,48) (6,43,17,49) (7,44,13,51) (8,40,15,52) (9,39,14,47) (19,55,28,64) (20,63,30,68) (21,59,29,72) (22,60,34,71) (23,56,36,66) (24,61,35,67) (25,62,31,69) (26,58,33,70) (27,57,32,65)
  (1,72,16,56) (2,64,18,61) (3,68,17,60) (4,67,13,58) (5,71,15,57) (6,66,14,62) (7,65,10,63) (8,69,12,59) (9,70,11,55) (19,54,34,38) (20,46,36,43) (21,50,35,42) (22,49,31,40) (23,53,33,39) (24,48,32,44) (25,47,28,45) (26,51,30,41) (27,52,29,37)
  (1,23,9,19,5,27) (2,24,7,20,6,25) (3,22,8,21,4,26) (10,32,18,28,14,36) (11,33,16,29,15,34) (12,31,17,30,13,35) (37,59,45,55,41,63) (38,60,43,56,42,61) (39,58,44,57,40,62) (46,68,54,64,50,72) (47,69,52,65,51,70) (48,67,53,66,49,71)