Properties

Genus \(15\)
Quotient Genus \(0\)
Group \(OD_{64}\)
Signature \([ 0; 2, 32, 32 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 15
Quotient Genus: 0
Group name: $OD_{64}$
Group identifier: [64,51]
Signature: $[ 0; 2, 32, 32 ]$
Conjugacy classes for this refined passport: 3, 25, 40

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:$E\times A_{2}\times A_{4}\times A_{4}^{2}$
Corresponding character(s): 6, 10, 17, 33

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

15.64-51.0.2-32-32.1.1

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