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