Properties

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

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Family Information

Genus: 14
Quotient Genus: 0
Group name: $C_{58}$
Group identifier: [58,2]
Signature: $[ 0; 2, 29, 58 ]$
Conjugacy classes for this refined passport: 2, 4, 44

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.

14.58-2.0.2-29-58.2.1

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