Properties

Genus \(7\)
Quotient Genus \(0\)
Group \(C_3\times D_9\)
Signature \([ 0; 2, 6, 9 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 7
Quotient Genus: 0
Group name: $C_3\times D_9$
Group identifier: [54,3]
Signature: $[ 0; 2, 6, 9 ]$
Conjugacy classes for this refined passport: 2, 8, 14

Jacobian variety group algebra decomposition:$E\times A_{3}^{2}$
Corresponding character(s): 3, 10

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):Yes
Trigonal automorphism: (1,10,19) (2,11,20) (3,12,21) (4,13,22) (5,14,23) (6,15,24) (7,16,25) (8,17,26) (9,18,27) (28,37,46) (29,38,47) (30,39,48) (31,40,49) (32,41,50) (33,42,51) (34,43,52) (35,44,53) (36,45,54)

Equation(s) of curve(s) in this refined passport:
  $y^3=x^9-1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

7.54-3.0.2-6-9.1.1

  (1,28) (2,30) (3,29) (4,35) (5,34) (6,36) (7,32) (8,31) (9,33) (10,37) (11,39) (12,38) (13,44) (14,43) (15,45) (16,41) (17,40) (18,42) (19,46) (20,48) (21,47) (22,53) (23,52) (24,54) (25,50) (26,49) (27,51)
  (1,43,19,34,10,52) (2,45,20,36,11,54) (3,44,21,35,12,53) (4,40,22,31,13,49) (5,42,23,33,14,51) (6,41,24,32,15,50) (7,37,25,28,16,46) (8,39,26,30,17,48) (9,38,27,29,18,47)
  (1,23,18,3,22,17,2,24,16) (4,26,11,6,25,10,5,27,12) (7,19,14,9,21,13,8,20,15) (28,50,45,30,49,44,29,51,43) (31,53,38,33,52,37,32,54,39) (34,46,41,36,48,40,35,47,42)