Passport invariants
| Degree: | $7$ |
| Monodromy group: | $A_7$ |
| Genus: | $0$ |
| Geometry type: | hyperbolic |
| Primitive: | yes |
Conjugacy class data
The order and cycle type of an element in each of the conjugacy classes $C_0, C_1, C_{\infty}$ of the passport containing this orbit.
| Order | Partition |
| $7$ | $7$ |
| $2$ | $2, 2, 1, 1, 1$ |
| $5$ | $5, 1, 1$ |
Galois orbits
| Passport size: | $2$ | |
| Number of Galois orbits: | $1$ |
| Label | Orbit size | Base field | Representative triple |
| a | $2$ | \(\Q(\sqrt{21}) \) ; Generator \(\nu\), with minimal polynomial \( T^{2} - T - 5 \). | $(1,2,7,6,5,4,3),(1,2)(3,4),(1,4,5,6,7)$ |