Family Information
| Genus: | $3$ |
| Quotient genus: | $0$ |
| Group name: | $D_4$ |
| Group identifier: | $[8,3]$ |
| Signature: | $[ 0; 2, 2, 2, 2, 2 ]$ |
| Conjugacy classes for this refined passport: | $2, 3, 3, 4, 4$ |
| Jacobian variety group algebra decomposition: | $E\times E^{2}$ |
| Corresponding character(s): | $4, 5$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $x^4 +y^4 +a_1x^2y^2 +a_2x^2 +a_2y^2 +1 = 0$ |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
3.8-3.0.2-2-2-2-2.1.1
| (1,2) (3,4) (5,6) (7,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,6) (2,5) (3,7) (4,8) |
3.8-3.0.2-2-2-2-2.1.2
| (1,2) (3,4) (5,6) (7,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,4) (2,3) (5,8) (6,7) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,5) (2,6) (3,8) (4,7) |
Displaying the unique representative of this refined passport up to braid equivalence.
3.8-3.0.2-2-2-2-2.1.1
| (1,2) (3,4) (5,6) (7,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,6) (2,5) (3,7) (4,8) |