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, 23, 48

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.

14.58-2.0.2-29-58.21.1

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