Properties

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

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $D_{12}$
Group identifier: [24,6]
Signature: $[ 0; 2, 2, 2, 2, 12 ]$
Conjugacy classes for this refined passport: 2, 2, 3, 4, 8

Jacobian variety group algebra decomposition:$A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s): 7, 8

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24)
Cyclic trigonal curve(s):No

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.24-6.0.2-2-2-2-12.1.1

  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24)
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24)
  (1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
  (1,20) (2,19) (3,21) (4,23) (5,22) (6,24) (7,14) (8,13) (9,15) (10,17) (11,16) (12,18)
  (1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)