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, 7, 20

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.

5.22-2.0.2-11-22.5.1

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