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: | $3, 5, 6, 12$ |
| 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.
5.24-14.0.2-2-2-6.5.1
| (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) (13,19) (14,20) (15,21) (16,22) (17,23) (18,24) | |
| (1,13) (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) | |
| (1,11,3,10,2,12) (4,8,6,7,5,9) (13,23,15,22,14,24) (16,20,18,19,17,21) |