Properties

Genus \(5\)
Quotient Genus \(0\)
Group \(D_6\)
Signature \([ 0; 2, 2, 2, 2, 3 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Quotient Genus: 0
Group name: $D_6$
Group identifier: [12,4]
Signature: $[ 0; 2, 2, 2, 2, 3 ]$
Conjugacy classes for this refined passport: 2, 2, 4, 4, 5

Jacobian variety group algebra decomposition:$E\times A_{2}^{2}$
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:
  $y^2=(x^{6}+a_{1}x^{3}+1)(x^{6}+a_{2}x^{3}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.12-4.0.2-2-2-2-3.2.1

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