Family Information
| Genus: | $3$ |
| Quotient genus: | $0$ |
| Group name: | $D_4$ |
| Group identifier: | $[8,3]$ |
| Signature: | $[ 0; 2, 2, 4, 4 ]$ |
| Conjugacy classes for this refined passport: | $3, 3, 5, 5$ |
The full automorphism group for this family is $C_2\times D_4$ with signature $[ 0; 2, 2, 2, 4 ]$.
| Jacobian variety group algebra decomposition: | $E\times E^{2}$ |
| Corresponding character(s): | $2, 5$ |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
3.8-3.0.2-2-4-4.1.1
| (1,3) (2,4) (5,7) (6,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,7,2,8) (3,6,4,5) | |
| (1,8,2,7) (3,5,4,6) |
3.8-3.0.2-2-4-4.1.2
| (1,3) (2,4) (5,7) (6,8) | |
| (1,4) (2,3) (5,8) (6,7) | |
| (1,7,2,8) (3,6,4,5) | |
| (1,7,2,8) (3,6,4,5) |
Displaying the unique representative of this refined passport up to braid equivalence.
3.8-3.0.2-2-4-4.1.1
| (1,3) (2,4) (5,7) (6,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,7,2,8) (3,6,4,5) | |
| (1,8,2,7) (3,5,4,6) |