Properties

Genus \(4\)
Quotient Genus \(0\)
Group \(C_{15}\)
Signature \([ 0; 3, 5, 15 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 4
Quotient Genus: 0
Group name: $C_{15}$
Group identifier: [15,1]
Signature: $[ 0; 3, 5, 15 ]$
Conjugacy classes for this refined passport: 2, 5, 12

Jacobian variety group algebra decomposition:$A_{4}$
Corresponding character(s): 5

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):Yes
Trigonal automorphism: (1,6,11) (2,7,12) (3,8,13) (4,9,14) (5,10,15)

Equation(s) of curve(s) in this refined passport:
  $y^3 = x^5-1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

4.15-1.0.3-5-15.2.1

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