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Let E be an elliptic curve with equation $y^2=x^3+Ax+B$.

The projection onto the $x$-coordinate is a Galois morphism of degree $2$.

But what about the projection onto the $y$-coordinate? Is it Galois of degree 3? Where does one study this map?

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    Are quadratic extensions (in char. 0, say) automatically Galois? What about a cubic extensions? If you can answer this then you'll answer your own question.2012-04-08

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