Properties

Genus \(8\)
Quotient Genus \(0\)
Group \(Q_8:S_3\)
Signature \([ 0; 2, 8, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Quotient Genus: 0
Group name: $Q_8:S_3$
Group identifier: [48,17]
Signature: $[ 0; 2, 8, 12 ]$
Conjugacy classes for this refined passport: 3, 8, 12

Jacobian variety group algebra decomposition:$E^{2}\times E^{2}\times E^{4}$
Corresponding character(s): 8, 10, 12

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):No

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.48-17.0.2-8-12.2.1

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