Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(C_3:Q_8\)
Signature \([ 0; 2, 4, 4, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $C_3:Q_8$
Group identifier: [24,4]
Signature: $[ 0; 2, 4, 4, 12 ]$
Conjugacy classes for this refined passport: 2, 5, 6, 8

Jacobian variety group algebra decomposition:$A_{4}\times A_{8}$
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:
  $y^2=x(x^{12}-1)(x^{12}+a_{1}x^{6}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.24-4.0.2-4-4-12.1.1

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