Properties

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

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Family Information

Genus: 4
Group name: $C_{18}$
Group identifier: [18,2]
Signature: $[ 0; 2, 9, 18 ]$
Conjugacy classes for this refined passport: 2, 9, 14

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.

4.18-2.0.2-9-18.3.1

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