Family Information
| Genus: | $4$ |
| Quotient genus: | $0$ |
| Group name: | $D_5$ |
| Group identifier: | $[10,1]$ |
| Signature: | $[ 0; 2, 2, 5, 5 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 4, 4$ |
The full automorphism group for this family is $D_{10}$ with signature $[ 0; 2, 2, 2, 5 ]$.
| Jacobian variety group algebra decomposition: | $A_{2}^{2}$ |
| Corresponding character(s): | $3$ |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
4.10-1.0.2-2-5-5.3.1
| (1,6) (2,10) (3,9) (4,8) (5,7) | |
| (1,6) (2,10) (3,9) (4,8) (5,7) | |
| (1,3,5,2,4) (6,8,10,7,9) | |
| (1,4,2,5,3) (6,9,7,10,8) |
4.10-1.0.2-2-5-5.3.2
| (1,6) (2,10) (3,9) (4,8) (5,7) | |
| (1,10) (2,9) (3,8) (4,7) (5,6) | |
| (1,4,2,5,3) (6,9,7,10,8) | |
| (1,4,2,5,3) (6,9,7,10,8) |
Displaying the unique representative of this refined passport up to braid equivalence.
4.10-1.0.2-2-5-5.3.1
| (1,6) (2,10) (3,9) (4,8) (5,7) | |
| (1,6) (2,10) (3,9) (4,8) (5,7) | |
| (1,3,5,2,4) (6,8,10,7,9) | |
| (1,4,2,5,3) (6,9,7,10,8) |