Properties

Genus \(13\)
Quotient Genus \(0\)
Group \(C_2.S_3^2\)
Signature \([ 0; 2, 12, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 13
Quotient Genus: 0
Group name: $C_2.S_3^2$
Group identifier: [72,21]
Signature: $[ 0; 2, 12, 12 ]$
Conjugacy classes for this refined passport: 3, 15, 17

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

Jacobian variety group algebra decomposition:$E\times E^{2}\times E^{2}\times E^{4}\times E^{4}$
Corresponding character(s): 5, 13, 14, 17, 18

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

13.72-21.0.2-12-12.1.1

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