Properties

Genus \(13\)
Small Group \(C_{54}\)
Signature \([ 0; 2, 27, 54 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more about

Family Information

Genus: 13
Group name: $C_{54}$
Group identifier: [54,2]
Signature: $[ 0; 2, 27, 54 ]$
Conjugacy classes for this refined passport: 2, 29, 40

Jacobian variety group algebra decomposition:$A_{9}\times A_{3}\times E$
Corresponding character(s): 4, 8, 20

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,28) (2,29) (3,30) (4,31) (5,32) (6,33) (7,34) (8,35) (9,36) (10,37) (11,38) (12,39) (13,40) (14,41) (15,42) (16,43) (17,44) (18,45) (19,46) (20,47) (21,48) (22,49) (23,50) (24,51) (25,52) (26,53) (27,54)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{27}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

13.54-2.0.2-27-54.11.1

  (1,28) (2,29) (3,30) (4,31) (5,32) (6,33) (7,34) (8,35) (9,36) (10,37) (11,38) (12,39) (13,40) (14,41) (15,42) (16,43) (17,44) (18,45) (19,46) (20,47) (21,48) (22,49) (23,50) (24,51) (25,52) (26,53) (27,54)
  (1,17,22,6,11,27,8,13,21,2,18,23,4,12,25,9,14,19,3,16,24,5,10,26,7,15,20) (28,44,49,33,38,54,35,40,48,29,45,50,31,39,52,36,41,46,30,43,51,32,37,53,34,42,47)
  (1,47,15,34,26,37,5,51,16,30,19,41,9,52,12,31,23,45,2,48,13,35,27,38,6,49,17,28,20,42,7,53,10,32,24,43,3,46,14,36,25,39,4,50,18,29,21,40,8,54,11,33,22,44)