Properties

Genus \(4\)
Quotient Genus \(0\)
Group \(C_3\times S_3\)
Signature \([ 0; 2, 2, 3, 3 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 4
Quotient Genus: 0
Group name: $C_3\times S_3$
Group identifier: [18,3]
Signature: $[ 0; 2, 2, 3, 3 ]$
Conjugacy classes for this refined passport: 2, 2, 4, 6

Jacobian variety group algebra decomposition:$A_{2}\times E^{2}$
Corresponding character(s): 3, 8

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)

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

4.18-3.0.2-2-3-3.2.1

  (1,10) (2,12) (3,11) (4,13) (5,15) (6,14) (7,16) (8,18) (9,17)
  (1,12) (2,11) (3,10) (4,15) (5,14) (6,13) (7,18) (8,17) (9,16)
  (1,7,4) (2,8,5) (3,9,6) (10,16,13) (11,17,14) (12,18,15)
  (1,5,9) (2,6,7) (3,4,8) (10,14,18) (11,15,16) (12,13,17)