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, 34, 47

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.

13.54-2.0.2-27-54.16.1

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