Properties

Genus \(3\)
Quotient Genus \(0\)
Group \(D_6\)
Signature \([ 0; 2, 2, 2, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 3
Quotient Genus: 0
Group name: $D_6$
Group identifier: [12,4]
Signature: $[ 0; 2, 2, 2, 6 ]$
Conjugacy classes for this refined passport: 2, 3, 3, 6

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

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:
  $y^2=x(x^{6}+a_{1}x^{3}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

3.12-4.0.2-2-2-6.1.1

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