Family Information
| Genus: | $4$ |
| Quotient genus: | $0$ |
| Group name: | $D_4$ |
| Group identifier: | $[8,3]$ |
| Signature: | $[ 0; 2, 2, 2, 2, 4 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 3, 4, 5$ |
| Jacobian variety group algebra decomposition: | $A_{2}^{2}$ |
| Corresponding character(s): | $5$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)$ | |
| $y^2=(x^{2}-1)(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
4.8-3.0.2-2-2-2-4.1.1
| (1,2) (3,4) (5,6) (7,8) | |
| (1,2) (3,4) (5,6) (7,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,5) (2,6) (3,8) (4,7) | |
| (1,7,2,8) (3,6,4,5) |