Properties

Genus \(4\)
Quotient Genus \(0\)
Group \(S_3\wr C_2\)
Signature \([ 0; 2, 4, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 4
Quotient Genus: 0
Group name: $S_3\wr C_2$
Group identifier: [72,40]
Signature: $[ 0; 2, 4, 6 ]$
Conjugacy classes for this refined passport: 3, 7, 8

Jacobian variety group algebra decomposition:$E^{4}$
Corresponding character(s): 8

Other Data

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

4.72-40.0.2-4-6.2.1

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