Family Information
| Genus: | $3$ |
| Quotient genus: | $0$ |
| Group name: | $C_2\times D_4$ |
| Group identifier: | $[16,11]$ |
| Signature: | $[ 0; 2, 2, 2, 4 ]$ |
| Conjugacy classes for this refined passport: | $4, 5, 8, 9$ |
| Jacobian variety group algebra decomposition: | $E\times E^{2}$ |
| Corresponding character(s): | $6, 9$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,4) (2,3) (5,8) (6,7) (9,12) (10,11) (13,16) (14,15) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{8}+a_1x^{4}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
3.16-11.0.2-2-2-4.6.1
| (1,4) (2,3) (5,8) (6,7) (9,12) (10,11) (13,16) (14,15) | |
| (1,5) (2,6) (3,7) (4,8) (9,13) (10,14) (11,15) (12,16) | |
| (1,11) (2,12) (3,9) (4,10) (5,16) (6,15) (7,14) (8,13) | |
| (1,14,2,13) (3,16,4,15) (5,9,6,10) (7,11,8,12) |