Properties

Genus \(4\)
Quotient Genus \(0\)
Group \(C_6\times S_3\)
Signature \([ 0; 2, 6, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 4
Quotient Genus: 0
Group name: $C_6\times S_3$
Group identifier: [36,12]
Signature: $[ 0; 2, 6, 6 ]$
Conjugacy classes for this refined passport: 3, 13, 18

Jacobian variety group algebra decomposition:$E\times E\times E^{2}$
Corresponding character(s): 6, 7, 16

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):Yes
Trigonal automorphism: (1,4,7) (2,5,8) (3,6,9) (10,13,16) (11,14,17) (12,15,18) (19,22,25) (20,23,26) (21,24,27) (28,31,34) (29,32,35) (30,33,36)

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

4.36-12.0.2-6-6.1.1

  (1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,25) (8,27) (9,26) (10,28) (11,30) (12,29) (13,31) (14,33) (15,32) (16,34) (17,36) (18,35)
  (1,14,9,10,5,18) (2,15,7,11,6,16) (3,13,8,12,4,17) (19,32,27,28,23,36) (20,33,25,29,24,34) (21,31,26,30,22,35)
  (1,35,4,29,7,32) (2,34,5,28,8,31) (3,36,6,30,9,33) (10,26,13,20,16,23) (11,25,14,19,17,22) (12,27,15,21,18,24)