Properties

Genus \(15\)
Quotient Genus \(0\)
Group \(C_2\times C_2^2:C_9\)
Signature \([ 0; 2, 18, 18 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 15
Quotient Genus: 0
Group name: $C_2\times C_2^2:C_9$
Group identifier: [72,16]
Signature: $[ 0; 2, 18, 18 ]$
Conjugacy classes for this refined passport: 3, 19, 24

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:$E^{3}\times A_{2}^{3}\times A_{2}^{3}$
Corresponding character(s): 19, 21, 22

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

15.72-16.0.2-18-18.1.1

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