Properties

Label 15.62-2.0.2-31-62.2
Genus \(15\)
Quotient genus \(0\)
Group \(C_{62}\)
Signature \([ 0; 2, 31, 62 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $15$
Quotient genus: $0$
Group name: $C_{62}$
Group identifier: $[62,2]$
Signature: $[ 0; 2, 31, 62 ]$
Conjugacy classes for this refined passport: $2, 4, 47$

Jacobian variety group algebra decomposition:$A_{15}$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,32) (2,33) (3,34) (4,35) (5,36) (6,37) (7,38) (8,39) (9,40) (10,41) (11,42) (12,43) (13,44) (14,45) (15,46) (16,47) (17,48) (18,49) (19,50) (20,51) (21,52) (22,53) (23,54) (24,55) (25,56) (26,57) (27,58) (28,59) (29,60) (30,61) (31,62)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{31}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.62-2.0.2-31-62.2.1

  (1,32) (2,33) (3,34) (4,35) (5,36) (6,37) (7,38) (8,39) (9,40) (10,41) (11,42) (12,43) (13,44) (14,45) (15,46) (16,47) (17,48) (18,49) (19,50) (20,51) (21,52) (22,53) (23,54) (24,55) (25,56) (26,57) (27,58) (28,59) (29,60) (30,61) (31,62)
  (1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30) (32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61)
  (1,61,28,57,24,53,20,49,16,45,12,41,8,37,4,33,31,60,27,56,23,52,19,48,15,44,11,40,7,36,3,32,30,59,26,55,22,51,18,47,14,43,10,39,6,35,2,62,29,58,25,54,21,50,17,46,13,42,9,38,5,34)