Family Information
| Genus: | $7$ |
| Quotient genus: | $0$ |
| Group name: | $C_4:C_4$ |
| Group identifier: | $[16,4]$ |
| Signature: | $[ 0; 2, 4, 4, 4 ]$ |
| Conjugacy classes for this refined passport: | $2, 6, 7, 10$ |
| Jacobian variety group algebra decomposition: | $E\times A_{2}\times A_{4}$ |
| Corresponding character(s): | $5, 6, 9$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=(x^{8}-1)(x^{8}+a_{1}x^{4}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
7.16-4.0.2-4-4-4.3.1
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) | |
| (1,6,3,8) (2,5,4,7) (9,14,11,16) (10,13,12,15) | |
| (1,9,2,10) (3,11,4,12) (5,15,6,16) (7,13,8,14) | |
| (1,16,2,15) (3,14,4,13) (5,12,6,11) (7,10,8,9) |