Database of Local Fields of positive characteristic

The table presents all isomorphism classes of degree 8 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^8 + 2*x^5 + x^4 + 2*x^2 + 2*x + 2 1 8 0 C8 ( 8T1 ) 8 1 [ ] 1 8
x^8 + t*x^6 + 2*t^4 2 4 4 C8 ( 8T1 ) 8 2 [ ] 2 4
x^8 + x^7 + (1 + t)*x^6 + x^4 + 2*x^3 + t^3*x^2 + t^3*x + 1 + t^2 + t^3 + t^4 2 4 4 C4×C2 ( 8T2 ) 8 2 [ ] 2 4
x^8 + t*x^4 + 2*t^2 4 2 6 C8×C2 ( 8T7 ) 16 4 [ ] 4 4
x^8 + t^2 4 2 6 Q8 ( 8T5 ) 8 4 [ ] 4 2
x^8 + 2*x^7 + 2*x^6 + 2*x^5 + (1 + 2*t)*x^4 + (1 + 2*t)*x^3 + 2*x^2 + (1 + 2*t)*x + 1 + t + t^2 4 2 6 D4 ( 8T4 ) 8 4 [ ] 4 2
x^8 + 2*t 8 1 7 QD16 ( 8T8 ) 16 8 [ ] 8 2
x^8 + t 8 1 7 QD16 ( 8T8 ) 16 8 [ ] 8 2
inserted by FC2 system