Family Information
| Genus: | $3$ |
| Quotient genus: | $0$ |
| Group name: | $D_4:C_4$ |
| Group identifier: | $[32,9]$ |
| Signature: | $[ 0; 2, 4, 8 ]$ |
| Conjugacy classes for this refined passport: | $5, 10, 11$ |
| Jacobian variety group algebra decomposition: | $E\times E^{2}$ |
| Corresponding character(s): | $6, 12$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) (13,15) (14,16) (17,19) (18,20) (21,23) (22,24) (25,27) (26,28) (29,31) (30,32) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{8}-1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
3.32-9.0.2-4-8.3.1
| (1,9) (2,10) (3,11) (4,12) (5,14) (6,13) (7,16) (8,15) (17,25) (18,26) (19,27) (20,28) (21,30) (22,29) (23,32) (24,31) | |
| (1,19,3,17) (2,20,4,18) (5,24,7,22) (6,23,8,21) (9,31,11,29) (10,32,12,30) (13,27,15,25) (14,28,16,26) | |
| (1,25,8,32,2,26,7,31) (3,27,6,30,4,28,5,29) (9,22,16,20,10,21,15,19) (11,24,14,18,12,23,13,17) |