Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(C_{12}\)
Signature \([ 0; 2, 2, 2, 2, 12, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $C_{12}$
Group identifier: [12,2]
Signature: $[ 0; 2, 2, 2, 2, 12, 12 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 2, 10, 11

Jacobian variety group algebra decomposition:$A_{4}\times A_{8}$
Corresponding character(s): 2, 6

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:
  $y^2=x(x^{24}+a_{1}x^{18}+a_{2}x^{12}+a_{3}x^{6}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.12-2.0.2-2-2-2-12-12.2.1

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