Properties

Label 14.14-2.0.2-2-2-2-14-14.1
Genus \(14\)
Quotient genus \(0\)
Group \(C_{14}\)
Signature \([ 0; 2, 2, 2, 2, 14, 14 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $14$
Quotient genus: $0$
Group name: $C_{14}$
Group identifier: $[14,2]$
Signature: $[ 0; 2, 2, 2, 2, 14, 14 ]$
Conjugacy classes for this refined passport: $2, 2, 2, 2, 9, 14$

Jacobian variety group algebra decomposition:$A_{2}\times A_{12}$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{28}+a_{1}x^{21}+a_{2}x^{14}+a_{3}x^{7}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.14-2.0.2-2-2-2-14-14.1.1

  (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14)
  (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14)
  (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14)
  (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14)
  (1,9,3,11,5,13,7,8,2,10,4,12,6,14)
  (1,14,6,12,4,10,2,8,7,13,5,11,3,9)