Database of Local Fields of positive characteristic

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
inserted by FC2 system