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: 2, 7, 9

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

Other Data

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

4.72-40.0.2-4-6.1.1

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