Family Information
| Genus: | $4$ |
| Quotient genus: | $0$ |
| Group name: | $C_{18}$ |
| Group identifier: | $[18,2]$ |
| Signature: | $[ 0; 2, 9, 18 ]$ |
| Conjugacy classes for this refined passport: | $2, 7, 18$ |
| Jacobian variety group algebra decomposition: | $A_{3}\times E$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{9}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
4.18-2.0.2-9-18.1.1
| (1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18) | |
| (1,4,7,2,5,8,3,6,9) (10,13,16,11,14,17,12,15,18) | |
| (1,18,6,12,8,14,2,16,4,10,9,15,3,17,5,11,7,13) |