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, 15

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.

5.48-14.0.2-4-12.5.1

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