Family Information
| Genus: | $10$ |
| Quotient genus: | $0$ |
| Group name: | $C_{10}$ |
| Group identifier: | $[10,2]$ |
| Signature: | $[ 0; 2, 2, 2, 2, 10, 10 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 2, 2, 8, 9$ |
| Jacobian variety group algebra decomposition: | $A_{2}\times A_{8}$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,6) (2,7) (3,8) (4,9) (5,10) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x(x^{20}+a_{1}x^{15}+a_{2}x^{10}+a_{3}x^{5}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
10.10-2.0.2-2-2-2-10-10.2.1
| (1,6) (2,7) (3,8) (4,9) (5,10) | |
| (1,6) (2,7) (3,8) (4,9) (5,10) | |
| (1,6) (2,7) (3,8) (4,9) (5,10) | |
| (1,6) (2,7) (3,8) (4,9) (5,10) | |
| (1,9,2,10,3,6,4,7,5,8) | |
| (1,8,5,7,4,6,3,10,2,9) |