Database of Local Fields of positive characteristic

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