Nagell-Lutz theorem

Statement
Let $$f(x) = x^3 + ax^2 + bx + c$$ with $$a,b,c \in \Z$$ such that the cubic curve $$y^2 = f(x)$$ is nonsingular. Let $$D$$ denote the discriminant of $$f$$. Then, if $$P$$ is a point having finite order in the elliptic curve group, the following are true:


 * If $$p$$ is not the point at infinity, then both its affine coordinates are integers
 * The $$y$$-coordinate of $$P$$ is either zero, or a divisor of $$D$$

Related results

 * Mordell-Weil theorem
 * Mazur's Theorem