Properties

Genus \(13\)
Quotient Genus \(0\)
Group \(C_3\times S_4\)
Signature \([ 0; 3, 4, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 13
Quotient Genus: 0
Group name: $C_3\times S_4$
Group identifier: [72,42]
Signature: $[ 0; 3, 4, 12 ]$
Conjugacy classes for this refined passport: 7, 9, 15

The full automorphism group for this family is $A_4\times S_4$ with signature $[ 0; 2, 3, 12 ]$.

Jacobian variety group algebra decomposition:$E\times E^{3}\times E^{3}\times A_{2}^{3}$
Corresponding character(s): 5, 11, 12, 14

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

13.72-42.0.3-4-12.1.1

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