Properties

Genus \(13\)
Quotient Genus \(0\)
Group \((C_2\times C_4).D_4\)
Signature \([ 0; 4, 4, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 13
Quotient Genus: 0
Group name: $(C_2\times C_4).D_4$
Group identifier: [64,20]
Signature: $[ 0; 4, 4, 8 ]$
Conjugacy classes for this refined passport: 13, 21, 26

Jacobian variety group algebra decomposition:$E\times E\times E\times A_{2}\times E^{2}\times E^{2}\times A_{2}^{2}$
Corresponding character(s): 9, 11, 12, 19, 21, 23, 26

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):No

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

13.64-20.0.4-4-8.1.1

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