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: 6, 8, 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.

3.48-48.0.2-4-6.2.1

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