Properties

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

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Family Information

Genus: 13
Quotient Genus: 0
Group name: $C_{54}$
Group identifier: [54,2]
Signature: $[ 0; 2, 27, 54 ]$
Conjugacy classes for this refined passport: 2, 19, 54

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.

13.54-2.0.2-27-54.1.1

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