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, 13, 53

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.

14.58-2.0.2-29-58.11.1

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