Properties

Label 6.26-2.0.2-13-26.6
Genus \(6\)
Quotient genus \(0\)
Group \(C_{26}\)
Signature \([ 0; 2, 13, 26 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $6$
Quotient genus: $0$
Group name: $C_{26}$
Group identifier: $[26,2]$
Signature: $[ 0; 2, 13, 26 ]$
Conjugacy classes for this refined passport: $2, 8, 18$

Jacobian variety group algebra decomposition:$A_{6}$
Corresponding character(s): $4$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,14) (2,15) (3,16) (4,17) (5,18) (6,19) (7,20) (8,21) (9,22) (10,23) (11,24) (12,25) (13,26)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{13}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

6.26-2.0.2-13-26.6.1

  (1,14) (2,15) (3,16) (4,17) (5,18) (6,19) (7,20) (8,21) (9,22) (10,23) (11,24) (12,25) (13,26)
  (1,7,13,6,12,5,11,4,10,3,9,2,8) (14,20,26,19,25,18,24,17,23,16,22,15,21)
  (1,21,2,22,3,23,4,24,5,25,6,26,7,14,8,15,9,16,10,17,11,18,12,19,13,20)