Family Information
| Genus: | $14$ |
| Quotient genus: | $0$ |
| Group name: | $\SL(2,3)$ |
| Group identifier: | $[24,3]$ |
| Signature: | $[ 0; 2, 2, 3, 3, 4 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 3, 4, 5$ |
| Jacobian variety group algebra decomposition: | $A_{6}\times A_{4}^{2}$ |
| 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: |
| $y^2=x(x^4-1)(x^{12}-a_{1}x^{10}-33x^8+2a_{1}x^6-33x^4-a_{1}x^2+1)(x^{12}-a_{2}x^{10}-33x^8+2a_{2}x^6-33x^4-a_{2}x^2+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
14.24-3.0.2-2-3-3-4.1.1
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) | |
| (1,2) (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) | |
| (1,7,2,8) (3,5,4,6) (9,15,10,16) (11,13,12,14) (17,23,18,24) (19,21,20,22) |