Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(C_3\times C_3:D_4\)
Signature \([ 0; 2, 6, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_3\times C_3:D_4$
Group identifier: [72,30]
Signature: $[ 0; 2, 6, 12 ]$
Conjugacy classes for this refined passport: 4, 20, 27

The full automorphism group for this family is $(C_3\times A_4):C_6$ with signature $[ 0; 2, 3, 12 ]$.

Jacobian variety group algebra decomposition:$E\times E\times E^{2}\times E^{2}\times E^{2}\times E^{2}$
Corresponding character(s): 5, 6, 16, 18, 19, 22

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.72-30.0.2-6-12.1.1

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