Properties

Label 14.12-5.0.2-2-2-2-2-6-6.45
Genus \(14\)
Quotient genus \(0\)
Group \(C_2\times C_6\)
Signature \([ 0; 2, 2, 2, 2, 2, 6, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $14$
Quotient genus: $0$
Group name: $C_2\times C_6$
Group identifier: $[12,5]$
Signature: $[ 0; 2, 2, 2, 2, 2, 6, 6 ]$
Conjugacy classes for this refined passport: $4, 4, 4, 4, 4, 8, 9$

Jacobian variety group algebra decomposition:$A_{2}\times A_{2}\times A_{5}\times A_{5}$
Corresponding character(s): $2, 3, 6, 7$

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{30}+a_{1}x^{24}+a_{2}x^{18}+a_{3}x^{12}+a_{4}x^{6}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.12-5.0.2-2-2-2-2-6-6.45.1

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