Let there be a curve $\Gamma$ in $\mathbb{C}^2$, which is an elliptic curve. Let there be another curve in $\mathbb{C}^2$, say $\Gamma$'. such that I have a bijection between the two curves, f : $\Gamma$ $\to$ $\Gamma$', such that f(u,v) = (u,v').
Then is $\Gamma$' also an elliptic curve ?