Family Information
| Genus: | $4$ |
| Quotient genus: | $0$ |
| Group name: | $S_3$ |
| Group identifier: | $[6,1]$ |
| Signature: | $[ 0; 2, 2, 3, 3, 3 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 3, 3, 3$ |
| Jacobian variety group algebra decomposition: | $A_{2}^{2}$ |
| 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 4 of 4 generating vectors for this refined passport.
4.6-1.0.2-2-3-3-3.1.1
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) | |
| (1,2,3) (4,5,6) | |
| (1,2,3) (4,5,6) | |
| (1,2,3) (4,5,6) |
4.6-1.0.2-2-3-3-3.1.2
| (1,4) (2,6) (3,5) | |
| (1,6) (2,5) (3,4) | |
| (1,2,3) (4,5,6) | |
| (1,2,3) (4,5,6) | |
| (1,3,2) (4,6,5) |
4.6-1.0.2-2-3-3-3.1.3
| (1,4) (2,6) (3,5) | |
| (1,6) (2,5) (3,4) | |
| (1,2,3) (4,5,6) | |
| (1,3,2) (4,6,5) | |
| (1,2,3) (4,5,6) |
4.6-1.0.2-2-3-3-3.1.4
| (1,4) (2,6) (3,5) | |
| (1,6) (2,5) (3,4) | |
| (1,3,2) (4,6,5) | |
| (1,2,3) (4,5,6) | |
| (1,2,3) (4,5,6) |
Displaying the unique representative of this refined passport up to braid equivalence.
4.6-1.0.2-2-3-3-3.1.1
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) | |
| (1,2,3) (4,5,6) | |
| (1,2,3) (4,5,6) | |
| (1,2,3) (4,5,6) |