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: | $2, 2, 3, 6$ |
| 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.
6.18-1.0.2-2-3-9.3.1
| (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) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) | |
| (1,5,9,2,6,7,3,4,8) (10,14,18,11,15,16,12,13,17) |
6.18-1.0.2-2-3-9.3.2
| (1,10) (2,12) (3,11) (4,18) (5,17) (6,16) (7,15) (8,14) (9,13) | |
| (1,18) (2,17) (3,16) (4,15) (5,14) (6,13) (7,12) (8,11) (9,10) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) (13,15,14) (16,18,17) | |
| (1,5,9,2,6,7,3,4,8) (10,14,18,11,15,16,12,13,17) |
Displaying the unique representative of this refined passport up to braid equivalence.
6.18-1.0.2-2-3-9.3.1
| (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) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) | |
| (1,5,9,2,6,7,3,4,8) (10,14,18,11,15,16,12,13,17) |