Properties

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

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Family Information

Genus: 3
Group name: $C_4\times S_3$
Group identifier: [24,5]
Signature: $[ 0; 2, 4, 12 ]$
Conjugacy classes for this refined passport: 3, 9, 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.

3.24-5.0.2-4-12.2.1

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