Properties

Label 6.18-1.0.2-2-3-9.1
Genus \(6\)
Quotient genus \(0\)
Group \(D_9\)
Signature \([ 0; 2, 2, 3, 9 ]\)
Generating Vectors \(2\)

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Family Information

Genus: $6$
Quotient genus: $0$
Group name: $D_9$
Group identifier: $[18,1]$
Signature: $[ 0; 2, 2, 3, 9 ]$
Conjugacy classes for this refined passport: $2, 2, 3, 4$

Jacobian variety group algebra decomposition:$A_{3}^{2}$
Corresponding character(s): $4$

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) (13,14,15) (16,17,18)

Generating vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

6.18-1.0.2-2-3-9.1.1

  (1,10) (2,12) (3,11) (4,18) (5,17) (6,16) (7,15) (8,14) (9,13)
  (1,16) (2,18) (3,17) (4,13) (5,15) (6,14) (7,10) (8,12) (9,11)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11) (13,15,14) (16,18,17)
  (1,4,7,2,5,8,3,6,9) (10,13,16,11,14,17,12,15,18)

6.18-1.0.2-2-3-9.1.2
  (1,10) (2,12) (3,11) (4,18) (5,17) (6,16) (7,15) (8,14) (9,13)
  (1,17) (2,16) (3,18) (4,14) (5,13) (6,15) (7,11) (8,10) (9,12)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18)
  (1,4,7,2,5,8,3,6,9) (10,13,16,11,14,17,12,15,18)

Display number of generating vectors:

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

  6.18-1.0.2-2-3-9.1.1

  (1,10) (2,12) (3,11) (4,18) (5,17) (6,16) (7,15) (8,14) (9,13)
  (1,16) (2,18) (3,17) (4,13) (5,15) (6,14) (7,10) (8,12) (9,11)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11) (13,15,14) (16,18,17)
  (1,4,7,2,5,8,3,6,9) (10,13,16,11,14,17,12,15,18)