Database of Local Fields of positive characteristic

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
inserted by FC2 system