Properties

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

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Family Information

Genus: 13
Group name: $C_{54}$
Group identifier: [54,2]
Signature: $[ 0; 2, 27, 54 ]$
Conjugacy classes for this refined passport: 2, 35, 46

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.

13.54-2.0.2-27-54.17.1

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