### Computing power series local coordinates on an algebraic curve

Let's say I have an elliptic curve $E$ given by a Weierstrass equation in $x$ and $y$. Let's say I choose a uniformizer $t$ around a point $P$ on $E$.

Then is there a SAGE function that writes $x$ or $y$ as a power series in $t$ in a neighborhood of $P$?

Often, I might take something like $t=x$, so it's a matter of writing $y$.

Even more to the point, I want to take a differential form regular at $P$, say in the form $dx/y$ or $xdx/y$, and write it as a power series times $dt$?