Properties

Label 13.64-21.0.4-4-8.16
Genus \(13\)
Quotient genus \(0\)
Group \(C_4.C_4^2\)
Signature \([ 0; 4, 4, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $13$
Quotient genus: $0$
Group name: $C_4.C_4^2$
Group identifier: $[64,21]$
Signature: $[ 0; 4, 4, 8 ]$
Conjugacy classes for this refined passport: $14, 20, 28$

The full automorphism group for this family is $C_2^2.D_{16}$ with signature $[ 0; 2, 4, 16 ]$.

Jacobian variety group algebra decomposition:$E\times E\times E\times A_{2}\times A_{4}\times E^{2}\times E^{2}$
Corresponding character(s): $6, 8, 9, 17, 22, 23, 27$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

13.64-21.0.4-4-8.16.1

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