Etale map from a variety to an elliptic curve

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I read this sentence and I can't see why it is true. Let $E$ be an elliptic curve over an algebraically closed field $k$, $f\colon Y\to E$ an etale map; then $Y$ is also a curve over $k$.

Can someone explain me why? Is it only true for etale morphisms or also for a more generic class of morphisms?

Thank you!