Family Information
| Genus: | $4$ |
| Quotient genus: | $0$ |
| Group name: | $C_3:S_3$ |
| Group identifier: | $[18,4]$ |
| Signature: | $[ 0; 2, 2, 3, 3 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 3, 5$ |
The full automorphism group for this family is $S_3^2$ with signature $[ 0; 2, 2, 2, 3 ]$.
| Jacobian variety group algebra decomposition: | $E^{2}\times E^{2}$ |
| Corresponding character(s): | $3, 6$ |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
4.18-4.0.2-2-3-3.2.1
| (1,10) (2,12) (3,11) (4,16) (5,18) (6,17) (7,13) (8,15) (9,14) | |
| (1,16) (2,18) (3,17) (4,13) (5,15) (6,14) (7,10) (8,12) (9,11) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) (13,15,14) (16,18,17) | |
| (1,5,9) (2,6,7) (3,4,8) (10,14,18) (11,15,16) (12,13,17) |
4.18-4.0.2-2-3-3.2.2
| (1,10) (2,12) (3,11) (4,16) (5,18) (6,17) (7,13) (8,15) (9,14) | |
| (1,17) (2,16) (3,18) (4,14) (5,13) (6,15) (7,11) (8,10) (9,12) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) | |
| (1,5,9) (2,6,7) (3,4,8) (10,14,18) (11,15,16) (12,13,17) |
Displaying the unique representative of this refined passport up to braid equivalence.
4.18-4.0.2-2-3-3.2.1
| (1,10) (2,12) (3,11) (4,16) (5,18) (6,17) (7,13) (8,15) (9,14) | |
| (1,16) (2,18) (3,17) (4,13) (5,15) (6,14) (7,10) (8,12) (9,11) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) (13,15,14) (16,18,17) | |
| (1,5,9) (2,6,7) (3,4,8) (10,14,18) (11,15,16) (12,13,17) |