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: 3, 7, 8

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.

4.15-1.0.3-5-15.8.1

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