Family Information
| Genus: | $3$ |
| Quotient genus: | $0$ |
| Group name: | $C_2^3$ |
| Group identifier: | $[8,5]$ |
| Signature: | $[ 0; 2, 2, 2, 2, 2 ]$ |
| Conjugacy classes for this refined passport: | $3, 3, 4, 5, 8$ |
| Jacobian variety group algebra decomposition: | $E\times E\times E$ |
| Corresponding character(s): | $4, 6, 8$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,3) (2,4) (5,7) (6,8) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
3.8-5.0.2-2-2-2-2.17.1
| (1,3) (2,4) (5,7) (6,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,4) (2,3) (5,8) (6,7) | |
| (1,5) (2,6) (3,7) (4,8) | |
| (1,8) (2,7) (3,6) (4,5) |