Properties

Label 5.22-2.0.2-11-22.4
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: $2, 6, 16$

Jacobian variety group algebra decomposition:$A_{5}$

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.

5.22-2.0.2-11-22.4.1

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