Properties

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

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Family Information

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

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.

4.15-1.0.3-5-15.1.1

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