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, 9

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.

12.24-4.0.2-4-4-12.2.1

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