Family Information
| Genus: | $3$ |
| Quotient genus: | $0$ |
| Group name: | $S_4$ |
| Group identifier: | $[24,12]$ |
| Signature: | $[ 0; 2, 2, 2, 3 ]$ |
| Conjugacy classes for this refined passport: | $2, 3, 3, 4$ |
| Jacobian variety group algebra decomposition: | $E^{3}$ |
| Corresponding character(s): | $4$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $x^4 +y^4 +a_1x^2y^2 +a_1x^2 +a_1y^2 +1 = 0$ |
Generating vector(s)
Displaying 3 of 3 generating vectors for this refined passport.
3.24-12.0.2-2-2-3.1.1
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) | |
| (1,13) (2,15) (3,14) (4,16) (5,21) (6,23) (7,22) (8,24) (9,17) (10,19) (11,18) (12,20) | |
| (1,21) (2,24) (3,23) (4,22) (5,17) (6,20) (7,19) (8,18) (9,13) (10,16) (11,15) (12,14) | |
| (1,6,11) (2,7,9) (3,5,10) (4,8,12) (13,18,23) (14,19,21) (15,17,22) (16,20,24) |
3.24-12.0.2-2-2-3.1.2
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) | |
| (1,13) (2,15) (3,14) (4,16) (5,21) (6,23) (7,22) (8,24) (9,17) (10,19) (11,18) (12,20) | |
| (1,17) (2,18) (3,20) (4,19) (5,13) (6,14) (7,16) (8,15) (9,21) (10,22) (11,24) (12,23) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) (13,22,20) (14,24,17) (15,23,19) (16,21,18) |
3.24-12.0.2-2-2-3.1.3
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) | |
| (1,17) (2,18) (3,20) (4,19) (5,13) (6,14) (7,16) (8,15) (9,21) (10,22) (11,24) (12,23) | |
| (1,13) (2,15) (3,14) (4,16) (5,21) (6,23) (7,22) (8,24) (9,17) (10,19) (11,18) (12,20) | |
| (1,6,11) (2,7,9) (3,5,10) (4,8,12) (13,18,23) (14,19,21) (15,17,22) (16,20,24) |
Displaying the unique representative of this refined passport up to braid equivalence.
3.24-12.0.2-2-2-3.1.1
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) | |
| (1,13) (2,15) (3,14) (4,16) (5,21) (6,23) (7,22) (8,24) (9,17) (10,19) (11,18) (12,20) | |
| (1,21) (2,24) (3,23) (4,22) (5,17) (6,20) (7,19) (8,18) (9,13) (10,16) (11,15) (12,14) | |
| (1,6,11) (2,7,9) (3,5,10) (4,8,12) (13,18,23) (14,19,21) (15,17,22) (16,20,24) |