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: | $3, 6, 7, 9$ |
| Jacobian variety group algebra decomposition: | $E\times E^{2}$ |
| Corresponding character(s): | $6, 9$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) (13,15) (14,16) |
| 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.
3.16-11.0.2-2-2-4.3.1
| (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) (13,15) (14,16) | |
| (1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14) | |
| (1,9) (2,10) (3,11) (4,12) (5,14) (6,13) (7,16) (8,15) | |
| (1,13,2,14) (3,15,4,16) (5,10,6,9) (7,12,8,11) |