Properties

Genus \(8\)
Small Group \(C_3\times D_8\)
Signature \([ 0; 2, 6, 24 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Group name: $C_3\times D_8$
Group identifier: [48,25]
Signature: $[ 0; 2, 6, 24 ]$
Conjugacy classes for this refined passport: 3, 12, 19

Jacobian variety group algebra decomposition:$E\times E\times E^{2}\times A_{2}^{2}$
Corresponding character(s): 5, 6, 14, 18

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):Yes
Trigonal automorphism: (1,5,9) (2,6,10) (3,7,11) (4,8,12) (13,17,21) (14,18,22) (15,19,23) (16,20,24) (25,29,33) (26,30,34) (27,31,35) (28,32,36) (37,41,45) (38,42,46) (39,43,47) (40,44,48)

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.48-25.0.2-6-24.1.1

  (1,13) (2,14) (3,16) (4,15) (5,17) (6,18) (7,20) (8,19) (9,21) (10,22) (11,24) (12,23) (25,37) (26,38) (27,40) (28,39) (29,41) (30,42) (31,44) (32,43) (33,45) (34,46) (35,48) (36,47)
  (1,30,9,26,5,34) (2,29,10,25,6,33) (3,31,11,27,7,35) (4,32,12,28,8,36) (13,44,21,40,17,48) (14,43,22,39,18,47) (15,42,23,38,19,46) (16,41,24,37,20,45)
  (1,46,8,39,10,41,3,48,5,38,12,43,2,45,7,40,9,42,4,47,6,37,11,44) (13,35,20,25,22,32,15,34,17,27,24,29,14,36,19,26,21,31,16,33,18,28,23,30)