Family Information
| Genus: | $7$ |
| Quotient genus: | $0$ |
| Group name: | $C_{30}$ |
| Group identifier: | $[30,4]$ |
| Signature: | $[ 0; 2, 15, 30 ]$ |
| Conjugacy classes for this refined passport: | $2, 15, 30$ |
| Jacobian variety group algebra decomposition: | $E\times A_{2}\times A_{4}$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,16) (2,17) (3,18) (4,19) (5,20) (6,21) (7,22) (8,23) (9,24) (10,25) (11,26) (12,27) (13,28) (14,29) (15,30) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{15}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
7.30-4.0.2-15-30.1.1
| (1,16) (2,17) (3,18) (4,19) (5,20) (6,21) (7,22) (8,23) (9,24) (10,25) (11,26) (12,27) (13,28) (14,29) (15,30) | |
| (1,7,13,4,10,11,2,8,14,5,6,12,3,9,15) (16,22,28,19,25,26,17,23,29,20,21,27,18,24,30) | |
| (1,30,9,18,12,21,5,29,8,17,11,25,4,28,7,16,15,24,3,27,6,20,14,23,2,26,10,19,13,22) |