Properties

Label 15.12-2.0.2-2-2-2-2-12-12.1
Genus \(15\)
Quotient genus \(0\)
Group \(C_{12}\)
Signature \([ 0; 2, 2, 2, 2, 2, 12, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $15$
Quotient genus: $0$
Group name: $C_{12}$
Group identifier: $[12,2]$
Signature: $[ 0; 2, 2, 2, 2, 2, 12, 12 ]$
Conjugacy classes for this refined passport: $2, 2, 2, 2, 2, 9, 10$

Jacobian variety group algebra decomposition:$A_{5}\times A_{10}$

Other Data

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

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.12-2.0.2-2-2-2-2-12-12.1.1

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