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, 11, 18

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.

5.22-2.0.2-11-22.9.1

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