Properties

Genus \(15\)
Quotient Genus \(0\)
Group \(C_2.D_{16}\)
Signature \([ 0; 4, 4, 16 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 15
Quotient Genus: 0
Group name: $C_2.D_{16}$
Group identifier: [64,47]
Signature: $[ 0; 4, 4, 16 ]$
Conjugacy classes for this refined passport: 7, 9, 19

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:$E\times A_{2}\times A_{4}\times A_{8}$
Corresponding character(s): 5, 10, 13, 16

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

15.64-47.0.4-4-16.1.1

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