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Properties

Label 6.6-1.0.2-2-3-3-3-3.1
Genus \(6\)
Quotient genus \(0\)
Group \(S_3\)
Signature \([ 0; 2, 2, 3, 3, 3, 3 ]\)
Generating Vectors \(8\)

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Family Information

Genus: $6$
Quotient genus: $0$
Group name: $S_3$
Group identifier: $[6,1]$
Signature: $[ 0; 2, 2, 3, 3, 3, 3 ]$
Conjugacy classes for this refined passport: $2, 2, 3, 3, 3, 3$

Jacobian variety group algebra decomposition:$A_{3}^{2}$
Corresponding character(s): $3$

Other Data

Hyperelliptic curve(s):no
Cyclic trigonal curve(s):yes
Trigonal automorphism: (1,2,3) (4,5,6)

Generating vector(s)

Displaying 8 of 8 generating vectors for this refined passport.

6.6-1.0.2-2-3-3-3-3.1.1

  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,2,3) (4,5,6)
  (1,2,3) (4,5,6)
  (1,3,2) (4,6,5)
  (1,3,2) (4,6,5)

6.6-1.0.2-2-3-3-3-3.1.2
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,2,3) (4,5,6)
  (1,3,2) (4,6,5)
  (1,2,3) (4,5,6)
  (1,3,2) (4,6,5)

6.6-1.0.2-2-3-3-3-3.1.3
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,2,3) (4,5,6)
  (1,3,2) (4,6,5)
  (1,3,2) (4,6,5)
  (1,2,3) (4,5,6)

6.6-1.0.2-2-3-3-3-3.1.4
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,2,3) (4,5,6)
  (1,2,3) (4,5,6)
  (1,2,3) (4,5,6)
  (1,2,3) (4,5,6)

6.6-1.0.2-2-3-3-3-3.1.5
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,2,3) (4,5,6)
  (1,3,2) (4,6,5)
  (1,3,2) (4,6,5)
  (1,3,2) (4,6,5)

6.6-1.0.2-2-3-3-3-3.1.6
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,3,2) (4,6,5)
  (1,2,3) (4,5,6)
  (1,3,2) (4,6,5)
  (1,3,2) (4,6,5)

6.6-1.0.2-2-3-3-3-3.1.7
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,3,2) (4,6,5)
  (1,3,2) (4,6,5)
  (1,2,3) (4,5,6)
  (1,3,2) (4,6,5)

6.6-1.0.2-2-3-3-3-3.1.8
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,3,2) (4,6,5)
  (1,3,2) (4,6,5)
  (1,3,2) (4,6,5)
  (1,2,3) (4,5,6)

Display number of generating vectors:

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

  6.6-1.0.2-2-3-3-3-3.1.1

  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,2,3) (4,5,6)
  (1,2,3) (4,5,6)
  (1,3,2) (4,6,5)
  (1,3,2) (4,6,5)