The table presents all isomorphism classes of degree 9 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^9 + x^4 + 1 | 1 | 9 | 0 | C9 ( 9T1 ) | 9 | 1 | [ ] 1 9 |
x^9 + x^7 + (1 + t)*x^6 + x^5 + t*x^4 + (t + t^2)*x^3 + (1 + t)*x^2 + (1 + t)*x + 1 + t^2 | 3 | 3 | 6 | S3×C3 ( 9T4 ) | 18 | 3 | [ ] 3 6 |
x^9 + t | 9 | 1 | 8 | (C9:C3):C2 ( 9T10 ) | 54 | 9 | [ ] 9 6 |