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, 16

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.

7.54-3.0.2-6-9.2.1

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