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, 20, 36

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.

14.58-2.0.2-29-58.18.1

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