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: | $4, 5, 7, 9$ |
| 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: | (1,4) (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: |
| $y^2=(x^{4}-1)(x^{8}+a_{1}x^{4}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.16-3.0.2-2-4-4.9.1
| (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) | |
| (1,9,2,10) (3,11,4,12) (5,15,6,16) (7,13,8,14) | |
| (1,15,4,14) (2,16,3,13) (5,9,8,12) (6,10,7,11) |