Family Information
| Genus: | $12$ |
| Quotient genus: | $0$ |
| Group name: | $C_3:Q_8$ |
| Group identifier: | $[24,4]$ |
| Signature: | $[ 0; 2, 4, 4, 12 ]$ |
| Conjugacy classes for this refined passport: | $2, 5, 6, 9$ |
| Jacobian variety group algebra decomposition: | $A_{4}\times A_{8}$ |
| Corresponding character(s): | $7, 8$ |
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: |
| $y^2=x(x^{12}-1)(x^{12}+a_{1}x^{6}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
12.24-4.0.2-4-4-12.2.1
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24) | |
| (1,13,4,16) (2,15,5,18) (3,14,6,17) (7,22,10,19) (8,24,11,21) (9,23,12,20) | |
| (1,21,4,24) (2,20,5,23) (3,19,6,22) (7,15,10,18) (8,14,11,17) (9,13,12,16) | |
| (1,11,6,7,2,12,4,8,3,10,5,9) (13,23,18,19,14,24,16,20,15,22,17,21) |