Properties

Genus \(5\)
Small Group \(C_{22}\)
Signature \([ 0; 2, 11, 22 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Group name: $C_{22}$
Group identifier: [22,2]
Signature: $[ 0; 2, 11, 22 ]$
Conjugacy classes for this refined passport: 2, 8, 15

Jacobian variety group algebra decomposition:$A_{5}$
Corresponding character(s): 4

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,12) (2,13) (3,14) (4,15) (5,16) (6,17) (7,18) (8,19) (9,20) (10,21) (11,22)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{11}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.22-2.0.2-11-22.6.1

  (1,12) (2,13) (3,14) (4,15) (5,16) (6,17) (7,18) (8,19) (9,20) (10,21) (11,22)
  (1,7,2,8,3,9,4,10,5,11,6) (12,18,13,19,14,20,15,21,16,22,17)
  (1,17,11,16,10,15,9,14,8,13,7,12,6,22,5,21,4,20,3,19,2,18)