Properties

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

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Family Information

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

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.

2.48-29.0.2-3-8.2.1

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