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, 6, 11

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.

4.15-1.0.3-5-15.7.1

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