Properties

Genus \(15\)
Quotient Genus \(0\)
Group \(C_7:C_{12}\)
Signature \([ 0; 3, 4, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 15
Quotient Genus: 0
Group name: $C_7:C_{12}$
Group identifier: [84,1]
Signature: $[ 0; 3, 4, 12 ]$
Conjugacy classes for this refined passport: 3, 5, 13

The full automorphism group for this family is $Q_8.F_7$ with signature $[ 0; 2, 3, 12 ]$.

Jacobian variety group algebra decomposition:$E\times A_{2}\times A_{4}^{3}$
Corresponding character(s): 3, 9, 14

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

15.84-1.0.3-4-12.1.1

  (1,15,29) (2,19,31) (3,16,33) (4,20,35) (5,17,30) (6,21,32) (7,18,34) (8,22,36) (9,26,38) (10,23,40) (11,27,42) (12,24,37) (13,28,39) (14,25,41) (43,57,71) (44,61,73) (45,58,75) (46,62,77) (47,59,72) (48,63,74) (49,60,76) (50,64,78) (51,68,80) (52,65,82) (53,69,84) (54,66,79) (55,70,81) (56,67,83)
  (1,45,8,52) (2,44,9,51) (3,43,10,50) (4,49,11,56) (5,48,12,55) (6,47,13,54) (7,46,14,53) (15,59,22,66) (16,58,23,65) (17,57,24,64) (18,63,25,70) (19,62,26,69) (20,61,27,68) (21,60,28,67) (29,73,36,80) (30,72,37,79) (31,71,38,78) (32,77,39,84) (33,76,40,83) (34,75,41,82) (35,74,42,81)
  (1,82,25,48,30,66,8,75,18,55,37,59) (2,80,22,47,32,69,9,73,15,54,39,62) (3,78,26,46,34,65,10,71,19,53,41,58) (4,83,23,45,29,68,11,76,16,52,36,61) (5,81,27,44,31,64,12,74,20,51,38,57) (6,79,24,43,33,67,13,72,17,50,40,60) (7,84,28,49,35,70,14,77,21,56,42,63)