Properties

Genus \(3\)
Quotient Genus \(0\)
Group \(\SL(2,3):C_2\)
Signature \([ 0; 2, 3, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 3
Quotient Genus: 0
Group name: $\SL(2,3):C_2$
Group identifier: [48,33]
Signature: $[ 0; 2, 3, 12 ]$
Conjugacy classes for this refined passport: 3, 4, 14

Jacobian variety group algebra decomposition:$E\times E^{2}$
Corresponding character(s): 3, 7

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^4 = x^3-1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

3.48-33.0.2-3-12.2.1

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