The table presents all isomorphism classes of degree 7 extensions of F3((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 + 2*x^2 + 1 | 1 | 7 | 0 | C7 ( 7T1 ) | 7 | 1 | [ ] 1 7 |
| x^7 + t | 7 | 1 | 6 | F7 ( 7T4 ) | 42 | 7 | [ ] 7 6 |