Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $C_2\times C_4$ |
| Group identifier: | $[8,2]$ |
| Signature: | $[ 0; 2, 2, 2, 4, 4 ]$ |
| Conjugacy classes for this refined passport: | $4, 4, 4, 5, 7$ |
| Jacobian variety group algebra decomposition: | $E\times A_{3}\times E$ |
| Corresponding character(s): | $2, 4, 6$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,4) (2,3) (5,8) (6,7) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{12}+a_{1}x^{8}+a_{2}x^{4}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.8-2.0.2-2-2-4-4.21.1
| (1,4) (2,3) (5,8) (6,7) | |
| (1,4) (2,3) (5,8) (6,7) | |
| (1,4) (2,3) (5,8) (6,7) | |
| (1,5,2,6) (3,7,4,8) | |
| (1,7,2,8) (3,5,4,6) |