Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(C_2.S_4\)
Signature \([ 0; 4, 6, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $C_2.S_4$
Group identifier: [48,28]
Signature: $[ 0; 4, 6, 8 ]$
Conjugacy classes for this refined passport: 5, 6, 8

Jacobian variety group algebra decomposition:$A_{4}\times A_{4}^{2}$
Corresponding character(s): 4, 8

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) (33,34) (35,36) (37,38) (39,40) (41,42) (43,44) (45,46) (47,48)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^4-1)(x^8+14x^4+1)(x^{12}-33x^8-33x^4+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.48-28.0.4-6-8.2.1

  (1,25,2,26) (3,29,4,30) (5,27,6,28) (7,32,8,31) (9,41,10,42) (11,45,12,46) (13,43,14,44) (15,48,16,47) (17,33,18,34) (19,37,20,38) (21,35,22,36) (23,40,24,39)
  (1,15,19,2,16,20) (3,10,24,4,9,23) (5,14,21,6,13,22) (7,11,18,8,12,17) (25,39,43,26,40,44) (27,34,48,28,33,47) (29,38,45,30,37,46) (31,35,42,32,36,41)
  (1,37,4,40,2,38,3,39) (5,35,8,33,6,36,7,34) (9,29,12,32,10,30,11,31) (13,27,16,25,14,28,15,26) (17,45,20,48,18,46,19,47) (21,43,24,41,22,44,23,42)