Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $C_2^2:C_4$ |
| Group identifier: | $[16,3]$ |
| Signature: | $[ 0; 2, 2, 4, 4 ]$ |
| Conjugacy classes for this refined passport: | $2, 5, 8, 10$ |
| Jacobian variety group algebra decomposition: | $A_{2}\times E\times E^{2}$ |
| 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: |
| $y^2=(x^{4}-1)(x^{8}+a_{1}x^{4}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.16-3.0.2-2-4-4.2.1
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) | |
| (1,5) (2,6) (3,7) (4,8) (9,13) (10,14) (11,15) (12,16) | |
| (1,10,2,9) (3,12,4,11) (5,16,6,15) (7,14,8,13) | |
| (1,14,4,15) (2,13,3,16) (5,12,8,9) (6,11,7,10) |