Family Information
| Genus: | $6$ |
| Quotient genus: | $0$ |
| Group name: | $C_8$ |
| Group identifier: | $[8,1]$ |
| Signature: | $[ 0; 2, 2, 2, 8, 8 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 2, 5, 6$ |
| Jacobian variety group algebra decomposition: | $A_{6}$ |
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: |
| $y^2=x(x^{12}+a_{1}x^{8}+a_{2}x^{4}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
6.8-1.0.2-2-2-8-8.1.1
| (1,2) (3,4) (5,6) (7,8) | |
| (1,2) (3,4) (5,6) (7,8) | |
| (1,2) (3,4) (5,6) (7,8) | |
| (1,5,3,7,2,6,4,8) | |
| (1,7,4,5,2,8,3,6) |