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) |
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) |