Properties

Genus \(8\)
Quotient Genus \(0\)
Group \(C_3:D_4\)
Signature \([ 0; 2, 2, 4, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Quotient Genus: 0
Group name: $C_3:D_4$
Group identifier: [24,8]
Signature: $[ 0; 2, 2, 4, 6 ]$
Conjugacy classes for this refined passport: 2, 4, 6, 8

Jacobian variety group algebra decomposition:$E^{2}\times A_{3}^{2}$
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:
  $y^2=(x^{6}-1)(x^{12}+a_{1}x^{6}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.24-8.0.2-2-4-6.1.1

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