Database of Local Fields of positive characteristic

The table presents all isomorphism classes of degree 4 extensions of F3((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^4 + 2*x^3 + 2 1 4 0 C4 ( 4T1 ) 4 1 [ ] 1 4
x^4 + t*x^2 + 2*t^2 2 2 2 C4 ( 4T1 ) 4 2 [ ] 2 2
x^4 + x^3 + (2 + 2*t)*x^2 + (2 + t)*x + 1 + t^2 2 2 2 C22 ( 4T2 ) 4 2 [ ] 2 2
x^4 + 2*t 4 1 3 D4 ( 4T3 ) 8 4 [ ] 4 2
x^4 + t 4 1 3 D4 ( 4T3 ) 8 4 [ ] 4 2
inserted by FC2 system