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, 25, 47

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.

14.58-2.0.2-29-58.23.1

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