Properties

Genus \(2\)
Small Group \(GL(2,3)\)
Signature \([ 0; 2, 3, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 2
Group name: $GL(2,3)$
Group identifier: [48,29]
Signature: $[ 0; 2, 3, 8 ]$
Conjugacy classes for this refined passport: 3, 4, 7

Jacobian variety group algebra decomposition:$E^{2}$
Corresponding character(s): 4

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:
  $y^2=x(x^4-1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

2.48-29.0.2-3-8.1.1

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