= 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>.
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