Family Information
| Genus: | $9$ |
| Quotient genus: | $0$ |
| Group name: | $C_2\times C_4$ |
| Group identifier: | $[8,2]$ |
| Signature: | $[ 0; 2, 2, 2, 2, 2, 4, 4 ]$ |
| Conjugacy classes for this refined passport: | $3, 3, 3, 3, 3, 5, 8$ |
| Jacobian variety group algebra decomposition: | $A_{2}\times A_{5}\times A_{2}$ |
| Corresponding character(s): | $2, 4, 6$ |
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: |
| $y^2=x^{20}+a_{1}x^{16}+a_{2}x^{12}+a_{3}x^{8}+a_{4}x^{4}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
9.8-2.0.2-2-2-2-2-4-4.39.1
| (1,3) (2,4) (5,7) (6,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,3) (2,4) (5,7) (6,8) | |
| (1,5,2,6) (3,7,4,8) | |
| (1,8,2,7) (3,6,4,5) |