Properties

Genus \(13\)
Quotient Genus \(0\)
Group \(S_3\times A_4\)
Signature \([ 0; 3, 6, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 13
Quotient Genus: 0
Group name: $S_3\times A_4$
Group identifier: [72,44]
Signature: $[ 0; 3, 6, 6 ]$
Conjugacy classes for this refined passport: 8, 11, 11

The full automorphism group for this family is $C_2\times S_3\times A_4$ with signature $[ 0; 2, 6, 6 ]$.

Jacobian variety group algebra decomposition:$E\times E\times E^{2}\times E^{3}\times E^{6}$
Corresponding character(s): 3, 5, 8, 10, 12

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

13.72-44.0.3-6-6.1.1

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