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: | $6, 10, 12$ |
| 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.
3.32-9.0.2-4-8.7.1
| (1,11) (2,12) (3,9) (4,10) (5,16) (6,15) (7,14) (8,13) (17,27) (18,28) (19,25) (20,26) (21,32) (22,31) (23,30) (24,29) | |
| (1,20,3,18) (2,19,4,17) (5,23,7,21) (6,24,8,22) (9,32,11,30) (10,31,12,29) (13,28,15,26) (14,27,16,25) | |
| (1,28,8,29,2,27,7,30) (3,26,6,31,4,25,5,32) (9,23,16,17,10,24,15,18) (11,21,14,19,12,22,13,20) |