Properties

Label 6.12-4.0.2-2-2-2-6.3
Genus \(6\)
Quotient genus \(0\)
Group \(D_6\)
Signature \([ 0; 2, 2, 2, 2, 6 ]\)
Generating Vectors \(9\)

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Family Information

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

Jacobian variety group algebra decomposition:$E\times E\times E^{2}\times E^{2}$
Corresponding character(s): $2, 4, 5, 6$

Other Data

Hyperelliptic curve(s):no
Cyclic trigonal curve(s):no

Generating vector(s)

Displaying 9 of 9 generating vectors for this refined passport.

6.12-4.0.2-2-2-2-6.3.1

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

6.12-4.0.2-2-2-2-6.3.2
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

6.12-4.0.2-2-2-2-6.3.3
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
  (1,5,3,4,2,6) (7,11,9,10,8,12)

6.12-4.0.2-2-2-2-6.3.4
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,5,3,4,2,6) (7,11,9,10,8,12)

6.12-4.0.2-2-2-2-6.3.5
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

6.12-4.0.2-2-2-2-6.3.6
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,5,3,4,2,6) (7,11,9,10,8,12)

6.12-4.0.2-2-2-2-6.3.7
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

6.12-4.0.2-2-2-2-6.3.8
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,6,2,4,3,5) (7,12,8,10,9,11)

6.12-4.0.2-2-2-2-6.3.9
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
  (1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
  (1,5,3,4,2,6) (7,11,9,10,8,12)

Display number of generating vectors:

Displaying the unique representative of this refined passport up to braid equivalence.

  6.12-4.0.2-2-2-2-6.3.1

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