Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(C_9\times S_3\)
Signature \([ 0; 2, 9, 18 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_9\times S_3$
Group identifier: [54,4]
Signature: $[ 0; 2, 9, 18 ]$
Conjugacy classes for this refined passport: 2, 16, 27

The full automorphism group for this family is $C_3^2:S_3:C_3$ with signature $[ 0; 2, 3, 18 ]$.

Jacobian variety group algebra decomposition:$E\times A_{3}\times A_{3}^{2}$
Corresponding character(s): 4, 10, 22

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.54-4.0.2-9-18.1.1

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