Properties

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

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Family Information

Genus: 14
Group name: $C_{58}$
Group identifier: [58,2]
Signature: $[ 0; 2, 29, 58 ]$
Conjugacy classes for this refined passport: 2, 30, 31

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.

14.58-2.0.2-29-58.28.1

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