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, 11, 18

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.

5.48-14.0.2-4-12.8.1

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