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, 27, 46

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.

14.58-2.0.2-29-58.25.1

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