Properties

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

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_3\times D_{12}$
Group identifier: [72,28]
Signature: $[ 0; 2, 6, 12 ]$
Conjugacy classes for this refined passport: 3, 18, 25

Jacobian variety group algebra decomposition:$E\times E\times E^{2}\times E^{2}\times A_{2}^{2}$
Corresponding character(s): 7, 10, 18, 20, 24

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):Yes
Trigonal automorphism: (1,7,13) (2,8,14) (3,9,15) (4,10,16) (5,11,17) (6,12,18) (19,25,31) (20,26,32) (21,27,33) (22,28,34) (23,29,35) (24,30,36) (37,43,49) (38,44,50) (39,45,51) (40,46,52) (41,47,53) (42,48,54) (55,61,67) (56,62,68) (57,63,69) (58,64,70) (59,65,71) (60,66,72)

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.72-28.0.2-6-12.1.1

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