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, 14, 17

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.

4.36-12.0.2-6-6.2.1

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