Properties

Genus \(3\)
Quotient Genus \(0\)
Group \(C_{14}\)
Signature \([ 0; 2, 7, 14 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 3
Quotient Genus: 0
Group name: $C_{14}$
Group identifier: [14,2]
Signature: $[ 0; 2, 7, 14 ]$
Conjugacy classes for this refined passport: 2, 3, 14

Jacobian variety group algebra decomposition:$A_{3}$
Corresponding character(s): 4

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{7}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

3.14-2.0.2-7-14.1.1

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