 Reduction certificate for a nonintegral elliptic point

On an integral Weierstrass equation of an elliptic curve with good reduction at a prime $p$, a nonidentity rational point reducing to the identity cannot have both coordinates integral at $p$. Indeed, an affine integral pair reduces to an affine point, distinct from the point at infinity. This can prove nonintegrality of a large linear combination without computing its coordinates. The nonidentity condition is essential and can often be checked using the known torsion subgroup.