Properties

Genus \(5\)
Quotient Genus \(0\)
Group \(D_6:C_4\)
Signature \([ 0; 2, 4, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Quotient Genus: 0
Group name: $D_6:C_4$
Group identifier: [48,14]
Signature: $[ 0; 2, 4, 12 ]$
Conjugacy classes for this refined passport: 6, 10, 16

Jacobian variety group algebra decomposition:$E\times E^{2}\times E^{2}$
Corresponding character(s): 6, 13, 15

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{12}-1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.48-14.0.2-4-12.6.1

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