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: 5, 11, 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.

5.48-14.0.2-4-12.4.1

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