Properties

Genus \(15\)
Quotient Genus \(0\)
Group \(C_2^2:D_9\)
Signature \([ 0; 4, 4, 9 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 15
Quotient Genus: 0
Group name: $C_2^2:D_9$
Group identifier: [72,15]
Signature: $[ 0; 4, 4, 9 ]$
Conjugacy classes for this refined passport: 5, 5, 7

The full automorphism group for this family is $C_2\times C_2^2:D_9$ with signature $[ 0; 2, 4, 18 ]$.

Jacobian variety group algebra decomposition:$E^{3}\times A_{2}^{6}$
Corresponding character(s): 8, 9

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

15.72-15.0.4-4-9.1.1

  (1,38,4,39) (2,40,3,37) (5,46,8,47) (6,48,7,45) (9,42,12,43) (10,44,11,41) (13,66,16,67) (14,68,15,65) (17,62,20,63) (18,64,19,61) (21,70,24,71) (22,72,23,69) (25,54,28,55) (26,56,27,53) (29,50,32,51) (30,52,31,49) (33,58,36,59) (34,60,35,57)
  (1,68,3,66) (2,65,4,67) (5,64,7,62) (6,61,8,63) (9,72,11,70) (10,69,12,71) (13,56,15,54) (14,53,16,55) (17,52,19,50) (18,49,20,51) (21,60,23,58) (22,57,24,59) (25,44,27,42) (26,41,28,43) (29,40,31,38) (30,37,32,39) (33,48,35,46) (34,45,36,47)
  (1,13,25,9,21,33,5,17,29) (2,16,27,10,24,35,6,20,31) (3,14,28,11,22,36,7,18,32) (4,15,26,12,23,34,8,19,30) (37,49,61,45,57,69,41,53,65) (38,52,63,46,60,71,42,56,67) (39,50,64,47,58,72,43,54,68) (40,51,62,48,59,70,44,55,66)