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Where does this clever choice of differential come from? (calculating $\mathrm{H}^1_{\mathrm{dR}}(E/k))$
In these notes of Kedlaya, he calculates the de Rham cohomology of an affine part $X$ of an elliptic curve $E$ over a field $K$, given by $y^2 = P(x) = x^3 + ax + b$.
He uses these relations:
$0 = y^...
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