Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $D_6$ |
| Group identifier: | $[12,4]$ |
| Signature: | $[ 0; 2, 2, 6, 6 ]$ |
| Conjugacy classes for this refined passport: | $4, 4, 6, 6$ |
The full automorphism group for this family is $C_2\times D_6$ with signature $[ 0; 2, 2, 2, 6 ]$.
| Jacobian variety group algebra decomposition: | $E\times E^{2}\times E^{2}$ |
| Corresponding character(s): | $3, 5, 6$ |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
5.12-4.0.2-2-6-6.2.1
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,5,3,4,2,6) (7,11,9,10,8,12) | |
| (1,6,2,4,3,5) (7,12,8,10,9,11) |
5.12-4.0.2-2-6-6.2.2
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) | |
| (1,6,2,4,3,5) (7,12,8,10,9,11) | |
| (1,6,2,4,3,5) (7,12,8,10,9,11) |
Displaying the unique representative of this refined passport up to braid equivalence.
5.12-4.0.2-2-6-6.2.1
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,5,3,4,2,6) (7,11,9,10,8,12) | |
| (1,6,2,4,3,5) (7,12,8,10,9,11) |