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, 33, 38

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.

13.54-2.0.2-27-54.15.1

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