Family Information
| Genus: | $4$ |
| Quotient genus: | $0$ |
| Group name: | $C_{15}$ |
| Group identifier: | $[15,1]$ |
| Signature: | $[ 0; 3, 5, 15 ]$ |
| Conjugacy classes for this refined passport: | $2, 5, 12$ |
| Jacobian variety group algebra decomposition: | $A_{4}$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | yes |
| Trigonal automorphism: | (1,6,11) (2,7,12) (3,8,13) (4,9,14) (5,10,15) |
| Equation(s) of curve(s) in this refined passport: |
| $y^3 = x^5-1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
4.15-1.0.3-5-15.2.1
| (1,6,11) (2,7,12) (3,8,13) (4,9,14) (5,10,15) | |
| (1,3,5,2,4) (6,8,10,7,9) (11,13,15,12,14) | |
| (1,14,7,5,13,6,4,12,10,3,11,9,2,15,8) |