Family Information
| Genus: | $3$ |
| Quotient genus: | $0$ |
| Group name: | $C_4\times S_3$ |
| Group identifier: | $[24,5]$ |
| Signature: | $[ 0; 2, 4, 12 ]$ |
| Conjugacy classes for this refined passport: | $3, 8, 12$ |
| Jacobian variety group algebra decomposition: | $E\times E^{2}$ |
| Corresponding character(s): | $6, 11$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x(x^{6}-1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
3.24-5.0.2-4-12.1.1
| (1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,19) (8,21) (9,20) (10,22) (11,24) (12,23) | |
| (1,21,4,24) (2,20,5,23) (3,19,6,22) (7,18,10,15) (8,17,11,14) (9,16,12,13) | |
| (1,11,6,7,2,12,4,8,3,10,5,9) (13,23,18,19,14,24,16,20,15,22,17,21) |