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, 10, 41

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.

14.58-2.0.2-29-58.8.1

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