The table presents all isomorphism classes of degree 7 extensions of F5((t)).
The data includes Defining polynomial, ramification index e, inertia degree f, valuation of discriminant c, Galois group G, Inertia Group I, Galois Slope Content.
| Defining Polynomial | e | f | c | Galois Group | #G | #I | Galois Slope Content |
|---|---|---|---|---|---|---|---|
| x^7 + 3*x + 3 | 1 | 7 | 0 | C7 (7T1) | 7 | 1 | [ ] 1 7 |
| x^7 + t | 7 | 1 | 6 | F7 (7T4) | 42 | 7 | [ ] 7 6 |