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: | $2, 6, 8, 12$ |
| 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: | (1,4) (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: |
| $y^2=x^{12}+a_1x^{6}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.24-14.0.2-2-2-6.4.1
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24) | |
| (1,16) (2,18) (3,17) (4,13) (5,15) (6,14) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20) | |
| (1,24) (2,23) (3,22) (4,21) (5,20) (6,19) (7,18) (8,17) (9,16) (10,15) (11,14) (12,13) | |
| (1,11,3,10,2,12) (4,8,6,7,5,9) (13,23,15,22,14,24) (16,20,18,19,17,21) |