# Can elliptic curve over imperfect field be reduced to Weierstrass form?

I have been reading 'The Arithmetic of Elliptic Curves' by Silverman.

It proves that any elliptic curve defined over a perfect field can be reduced to Weierstrass form, [III.3.1,page 59]. The convention $$k$$ is perfect is mentioned at the begining of the book.

The proof uses the fact that $$\bar{k}/k$$ is Galois when $$k$$ is perfect.

Hence I don't know how to move the proof to the case $$k$$ is imperfect.