Properties

Genus \(14\)
Quotient Genus \(0\)
Group \(C_{58}\)
Signature \([ 0; 2, 29, 58 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 14
Quotient Genus: 0
Group name: $C_{58}$
Group identifier: [58,2]
Signature: $[ 0; 2, 29, 58 ]$
Conjugacy classes for this refined passport: 2, 22, 35

Jacobian variety group algebra decomposition:$A_{14}$
Corresponding character(s): 4

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,30) (2,31) (3,32) (4,33) (5,34) (6,35) (7,36) (8,37) (9,38) (10,39) (11,40) (12,41) (13,42) (14,43) (15,44) (16,45) (17,46) (18,47) (19,48) (20,49) (21,50) (22,51) (23,52) (24,53) (25,54) (26,55) (27,56) (28,57) (29,58)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{29}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

14.58-2.0.2-29-58.20.1

  (1,30) (2,31) (3,32) (4,33) (5,34) (6,35) (7,36) (8,37) (9,38) (10,39) (11,40) (12,41) (13,42) (14,43) (15,44) (16,45) (17,46) (18,47) (19,48) (20,49) (21,50) (22,51) (23,52) (24,53) (25,54) (26,55) (27,56) (28,57) (29,58)
  (1,21,12,3,23,14,5,25,16,7,27,18,9,29,20,11,2,22,13,4,24,15,6,26,17,8,28,19,10) (30,50,41,32,52,43,34,54,45,36,56,47,38,58,49,40,31,51,42,33,53,44,35,55,46,37,57,48,39)
  (1,39,19,57,8,46,26,35,15,53,4,42,22,31,11,49,29,38,18,56,7,45,25,34,14,52,3,41,21,30,10,48,28,37,17,55,6,44,24,33,13,51,2,40,20,58,9,47,27,36,16,54,5,43,23,32,12,50)