Properties

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

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Family Information

Genus: 5
Quotient Genus: 0
Group name: $C_{22}$
Group identifier: [22,2]
Signature: $[ 0; 2, 11, 22 ]$
Conjugacy classes for this refined passport: 2, 10, 14

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.

5.22-2.0.2-11-22.8.1

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