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, 23, 52

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.

13.54-2.0.2-27-54.5.1

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