Family Information
| Genus: | $8$ |
| Quotient genus: | $0$ |
| Group name: | $\SL(2,3)$ |
| Group identifier: | $[24,3]$ |
| Signature: | $[ 0; 2, 3, 3, 4 ]$ |
| Conjugacy classes for this refined passport: | $2, 3, 4, 5$ |
| Jacobian variety group algebra decomposition: | $A_{4}\times A_{2}^{2}$ |
| Corresponding character(s): | $4, 5$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x(x^4-1)(x^{12}-a_{1}x^{10}-33x^8+2a_{1}x^6-33x^4-a_{1}x^2+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
8.24-3.0.2-3-3-4.1.1
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) | |
| (1,9,17) (2,10,18) (3,15,21) (4,16,22) (5,11,23) (6,12,24) (7,13,19) (8,14,20) | |
| (1,24,13) (2,23,14) (3,19,11) (4,20,12) (5,17,16) (6,18,15) (7,22,10) (8,21,9) | |
| (1,8,2,7) (3,6,4,5) (9,16,10,15) (11,14,12,13) (17,24,18,23) (19,22,20,21) |