Properties

Genus \(13\)
Quotient Genus \(0\)
Group \(C_3\times D_{13}\)
Signature \([ 0; 2, 6, 39 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 13
Quotient Genus: 0
Group name: $C_3\times D_{13}$
Group identifier: [78,4]
Signature: $[ 0; 2, 6, 39 ]$
Conjugacy classes for this refined passport: 2, 5, 14

Jacobian variety group algebra decomposition:$E\times A_{6}^{2}$
Corresponding character(s): 4, 13

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):Yes
Trigonal automorphism: (1,27,14) (2,28,15) (3,29,16) (4,30,17) (5,31,18) (6,32,19) (7,33,20) (8,34,21) (9,35,22) (10,36,23) (11,37,24) (12,38,25) (13,39,26) (40,66,53) (41,67,54) (42,68,55) (43,69,56) (44,70,57) (45,71,58) (46,72,59) (47,73,60) (48,74,61) (49,75,62) (50,76,63) (51,77,64) (52,78,65)

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

13.78-4.0.2-6-39.1.1

  (1,40) (2,52) (3,51) (4,50) (5,49) (6,48) (7,47) (8,46) (9,45) (10,44) (11,43) (12,42) (13,41) (14,53) (15,65) (16,64) (17,63) (18,62) (19,61) (20,60) (21,59) (22,58) (23,57) (24,56) (25,55) (26,54) (27,66) (28,78) (29,77) (30,76) (31,75) (32,74) (33,73) (34,72) (35,71) (36,70) (37,69) (38,68) (39,67)
  (1,55,27,42,14,68) (2,54,28,41,15,67) (3,53,29,40,16,66) (4,65,30,52,17,78) (5,64,31,51,18,77) (6,63,32,50,19,76) (7,62,33,49,20,75) (8,61,34,48,21,74) (9,60,35,47,22,73) (10,59,36,46,23,72) (11,58,37,45,24,71) (12,57,38,44,25,70) (13,56,39,43,26,69)
  (1,38,23,8,32,17,2,39,24,9,33,18,3,27,25,10,34,19,4,28,26,11,35,20,5,29,14,12,36,21,6,30,15,13,37,22,7,31,16) (40,77,62,47,71,56,41,78,63,48,72,57,42,66,64,49,73,58,43,67,65,50,74,59,44,68,53,51,75,60,45,69,54,52,76,61,46,70,55)