Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $C_2\times D_6$ |
| Group identifier: | $[24,14]$ |
| Signature: | $[ 0; 2, 2, 2, 6 ]$ |
| Conjugacy classes for this refined passport: | $3, 6, 7, 10$ |
| Jacobian variety group algebra decomposition: | $E\times E^{2}\times E^{2}$ |
| Corresponding character(s): | $3, 9, 12$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) (13,19) (14,20) (15,21) (16,22) (17,23) (18,24) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{12}+a_1x^{6}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.24-14.0.2-2-2-6.7.1
| (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) (13,19) (14,20) (15,21) (16,22) (17,23) (18,24) | |
| (1,16) (2,18) (3,17) (4,13) (5,15) (6,14) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20) | |
| (1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16) | |
| (1,5,3,4,2,6) (7,11,9,10,8,12) (13,17,15,16,14,18) (19,23,21,22,20,24) |