Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $A_4$ |
| Group identifier: | $[12,3]$ |
| Signature: | $[ 0; 3, 3, 3, 3 ]$ |
| Conjugacy classes for this refined passport: | $3, 3, 4, 4$ |
The full automorphism group for this family is $C_2\times S_4$ with signature $[ 0; 2, 2, 2, 3 ]$.
| Jacobian variety group algebra decomposition: | $A_{2}\times E^{3}$ |
| Corresponding character(s): | $2, 4$ |
Generating vector(s)
Displaying 5 of 5 generating vectors for this refined passport.
5.12-3.0.3-3-3-3.1.1
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,12,7) (2,10,6) (3,9,8) (4,11,5) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) |
5.12-3.0.3-3-3-3.1.2
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,7,12) (2,6,10) (3,8,9) (4,5,11) | |
| (1,9,5) (2,11,8) (3,12,6) (4,10,7) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) |
5.12-3.0.3-3-3-3.1.3
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,7,12) (2,6,10) (3,8,9) (4,5,11) | |
| (1,12,7) (2,10,6) (3,9,8) (4,11,5) | |
| (1,9,5) (2,11,8) (3,12,6) (4,10,7) |
5.12-3.0.3-3-3-3.1.4
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,7,12) (2,6,10) (3,8,9) (4,5,11) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) | |
| (1,12,7) (2,10,6) (3,9,8) (4,11,5) |
5.12-3.0.3-3-3-3.1.5
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,7,12) (2,6,10) (3,8,9) (4,5,11) | |
| (1,11,6) (2,9,7) (3,10,5) (4,12,8) | |
| (1,11,6) (2,9,7) (3,10,5) (4,12,8) |
Displaying 2 of 2 representatives for this refined passport up to braid equivalence.
5.12-3.0.3-3-3-3.1.1
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,12,7) (2,10,6) (3,9,8) (4,11,5) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) |
5.12-3.0.3-3-3-3.1.2
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,7,12) (2,6,10) (3,8,9) (4,5,11) | |
| (1,9,5) (2,11,8) (3,12,6) (4,10,7) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) |