Properties

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

Related objects

Downloads

Learn more about

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, 17

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.

5.48-14.0.2-4-12.7.1

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