Field Embeddings

[cm]

Hi,

suppose I have a field embedding A = GF(2^4) -> B = GF(2^20) say,
and I pick a homomorphism phi from C=A.Hom(GF(2^20,'x')), e.g.

sage: phi

Ring morphism:
From: Finite Field in x of size 2^4
To: Finite Field in x of size 2^20
Defn: x |--> x^19 + x^14 + x^13 + x^12 + x^10 + x^8 + x^2 + x

I can evaluate phi on any element from A, but I cannot evaluate the
inverse map.
Is there a way to calculate the inverse?

Thanks!