Properties

Genus \(3\)
Quotient Genus \(0\)
Group \(C_4\times S_3\)
Signature \([ 0; 2, 4, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 3
Quotient Genus: 0
Group name: $C_4\times S_3$
Group identifier: [24,5]
Signature: $[ 0; 2, 4, 12 ]$
Conjugacy classes for this refined passport: 4, 8, 11

Jacobian variety group algebra decomposition:$E\times E^{2}$
Corresponding character(s): 6, 11

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:
  $y^2=x(x^{6}-1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

3.24-5.0.2-4-12.3.1

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