The table presents all isomorphism classes of degree 5 extensions of F2((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^5 + x^2 + 1 | 1 | 5 | 0 | C5 ( 5T1 ) | 5 | 1 | [ ] 1 5 |
| x^5 + t | 5 | 1 | 4 | F5 ( 5T3 ) | 20 | 5 | [ ] 5 4 |