Properties

Genus \(15\)
Quotient Genus \(0\)
Group \(C_2\times C_{32}\)
Signature \([ 0; 2, 32, 32 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 15
Quotient Genus: 0
Group name: $C_2\times C_{32}$
Group identifier: [64,50]
Signature: $[ 0; 2, 32, 32 ]$
Conjugacy classes for this refined passport: 3, 33, 64

The full automorphism group for this family is $C_4.D_4:C_4$ with signature $[ 0; 2, 4, 32 ]$.

Jacobian variety group algebra decomposition:$A_{8}\times A_{4}\times A_{2}\times E$
Corresponding character(s): 4, 6, 10, 18

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

15.64-50.0.2-32-32.1.1

  (1,17) (2,18) (3,19) (4,20) (5,21) (6,22) (7,23) (8,24) (9,25) (10,26) (11,27) (12,28) (13,29) (14,30) (15,31) (16,32) (33,49) (34,50) (35,51) (36,52) (37,53) (38,54) (39,55) (40,56) (41,57) (42,58) (43,59) (44,60) (45,61) (46,62) (47,63) (48,64)
  (1,33,9,41,5,37,13,45,3,35,11,43,7,39,15,47,2,34,10,42,6,38,14,46,4,36,12,44,8,40,16,48) (17,49,25,57,21,53,29,61,19,51,27,59,23,55,31,63,18,50,26,58,22,54,30,62,20,52,28,60,24,56,32,64)
  (1,64,16,56,8,60,12,52,4,62,14,54,6,58,10,50,2,63,15,55,7,59,11,51,3,61,13,53,5,57,9,49) (17,48,32,40,24,44,28,36,20,46,30,38,22,42,26,34,18,47,31,39,23,43,27,35,19,45,29,37,21,41,25,33)