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Properties

Label 12.12-4.0.2-2-3-3-3-6.1
Genus \(12\)
Quotient genus \(0\)
Group \(D_6\)
Signature \([ 0; 2, 2, 3, 3, 3, 6 ]\)
Generating Vectors \(8\)

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Family Information

Genus: $12$
Quotient genus: $0$
Group name: $D_6$
Group identifier: $[12,4]$
Signature: $[ 0; 2, 2, 3, 3, 3, 6 ]$
Conjugacy classes for this refined passport: $3, 4, 5, 5, 5, 6$

Jacobian variety group algebra decomposition:$A_{3}^{2}\times A_{3}^{2}$
Corresponding character(s): $5, 6$

Other Data

Hyperelliptic curve(s):no
Cyclic trigonal curve(s):yes
Trigonal automorphism: (1,2,3) (4,5,6) (7,8,9) (10,11,12)

Generating vector(s)

Displaying 8 of 8 generating vectors for this refined passport.

12.12-4.0.2-2-3-3-3-6.1.1

  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-3-3-3-6.1.2
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-3-3-3-6.1.3
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-3-3-3-6.1.4
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-3-3-3-6.1.5
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-3-3-3-6.1.6
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-3-3-3-6.1.7
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-3-3-3-6.1.8
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,5,3,4,2,6) (7,11,9,10,8,12)

Display number of generating vectors: