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: | $4, 5, 6, 11$ |
| 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: | (1,10) (2,11) (3,12) (4,7) (5,8) (6,9) (13,22) (14,23) (15,24) (16,19) (17,20) (18,21) |
| 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.
5.24-14.0.2-2-2-6.9.1
| (1,10) (2,11) (3,12) (4,7) (5,8) (6,9) (13,22) (14,23) (15,24) (16,19) (17,20) (18,21) | |
| (1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,19) (8,21) (9,20) (10,22) (11,24) (12,23) | |
| (1,18) (2,17) (3,16) (4,15) (5,14) (6,13) (7,24) (8,23) (9,22) (10,21) (11,20) (12,19) | |
| (1,8,3,7,2,9) (4,11,6,10,5,12) (13,20,15,19,14,21) (16,23,18,22,17,24) |