Properties

Genus \(3\)
Quotient Genus \(0\)
Group \(C_9\)
Signature \([ 0; 3, 9, 9 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 3
Quotient Genus: 0
Group name: $C_9$
Group identifier: [9,1]
Signature: $[ 0; 3, 9, 9 ]$
Conjugacy classes for this refined passport: 2, 4, 7

Jacobian variety group algebra decomposition:$A_{3}$
Corresponding character(s): 2

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):Yes
Trigonal automorphism: (1,2,3) (4,5,6) (7,8,9)

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

3.9-1.0.3-9-9.1.1

  (1,2,3) (4,5,6) (7,8,9)
  (1,4,7,2,5,8,3,6,9)
  (1,8,4,3,7,6,2,9,5)