Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(C_3:C_4\)
Signature \([ 0; 2, 2, 2, 4, 4, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $C_3:C_4$
Group identifier: [12,1]
Signature: $[ 0; 2, 2, 2, 4, 4, 6 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 4, 5, 6

Jacobian variety group algebra decomposition:$A_{4}\times A_{8}$
Corresponding character(s): 3, 5

Other Data

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

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.12-1.0.2-2-2-4-4-6.1.1

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