Properties

Genus \(4\)
Quotient Genus \(0\)
Group \(C_{18}\)
Signature \([ 0; 2, 9, 18 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 4
Quotient Genus: 0
Group name: $C_{18}$
Group identifier: [18,2]
Signature: $[ 0; 2, 9, 18 ]$
Conjugacy classes for this refined passport: 2, 10, 17

Jacobian variety group algebra decomposition:$A_{3}\times E$
Corresponding character(s): 4, 8

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{9}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

4.18-2.0.2-9-18.4.1

  (1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18)
  (1,8,4,3,7,6,2,9,5) (10,17,13,12,16,15,11,18,14)
  (1,14,9,11,6,16,3,13,8,10,5,18,2,15,7,12,4,17)