Family Information
| Genus: | $4$ |
| Quotient genus: | $0$ |
| Group name: | $D_4$ |
| Group identifier: | $[8,3]$ |
| Signature: | $[ 0; 2, 2, 2, 2, 4 ]$ |
| Conjugacy classes for this refined passport: | $3, 4, 4, 4, 5$ |
| Jacobian variety group algebra decomposition: | $E\times E\times E^{2}$ |
| Corresponding character(s): | $3, 4, 5$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | no |
Generating vector(s)
Displaying 4 of 4 generating vectors for this refined passport.
4.8-3.0.2-2-2-2-4.3.1
| (1,3) (2,4) (5,7) (6,8) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,7,2,8) (3,6,4,5) |
4.8-3.0.2-2-2-2-4.3.2
| (1,3) (2,4) (5,7) (6,8) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,6) (2,5) (3,7) (4,8) | |
| (1,8,2,7) (3,5,4,6) |
4.8-3.0.2-2-2-2-4.3.3
| (1,3) (2,4) (5,7) (6,8) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,6) (2,5) (3,7) (4,8) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,8,2,7) (3,5,4,6) |
4.8-3.0.2-2-2-2-4.3.4
| (1,3) (2,4) (5,7) (6,8) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,6) (2,5) (3,7) (4,8) | |
| (1,6) (2,5) (3,7) (4,8) | |
| (1,7,2,8) (3,6,4,5) |
Displaying the unique representative of this refined passport up to braid equivalence.
4.8-3.0.2-2-2-2-4.3.1
| (1,3) (2,4) (5,7) (6,8) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,7,2,8) (3,6,4,5) |