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, 17, 51

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.

14.58-2.0.2-29-58.15.1

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