In general, projective closure of smooth affine curve is not always smooth projective curve.
But, what about projective closure of smooth affine curve defined by Weierstrass equation?
Let $E$ be a smooth affine curve （over field $K$） defined by $y^2 +a_1 xy+ a_3y =x^3 + a_2x^2 + a_4x + a_6$（all coefficients are in $K$）, then is the projective closure of $E$ is always smooth projective curve?
Thank you in advance.