Properties

Genus \(3\)
Small Group \(C_2\times S_4\)
Signature \([ 0; 2, 4, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 3
Group name: $C_2\times S_4$
Group identifier: [48,48]
Signature: $[ 0; 2, 4, 6 ]$
Conjugacy classes for this refined passport: 5, 9, 10

Jacobian variety group algebra decomposition:$E^{3}$
Corresponding character(s): 8

Other Data

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

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

3.48-48.0.2-4-6.1.1

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