Properties

Label 9.48-31.0.3-4-12.1
Genus \(9\)
Quotient genus \(0\)
Group \(C_4\times A_4\)
Signature \([ 0; 3, 4, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $9$
Quotient genus: $0$
Group name: $C_4\times A_4$
Group identifier: $[48,31]$
Signature: $[ 0; 3, 4, 12 ]$
Conjugacy classes for this refined passport: $5, 9, 16$

The full automorphism group for this family is $C_2^3.(C_2\times A_4)$ with signature $[ 0; 2, 3, 12 ]$.

Jacobian variety group algebra decomposition:$E\times A_{2}\times A_{2}^{3}$
Corresponding character(s): $4, 9, 15$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

9.48-31.0.3-4-12.1.1

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