Nagell-Lutz Theorem

The Nagell-Lutz theorem is a result in diophantine geometry about rational torsion points on elliptic curves defined by non-singular cubic equations with integer coefficients. It states that any rational point of finite order on such a curve either has both coordinates as integers, or has y-coordinate zero and so has order two, and that whenever the y-coordinate is nonzero it must divide the curve's discriminant. The theorem was discovered independently by the Norwegian mathematician Trygve Nagell, who published it in 1935, and by Elisabeth Lutz, who published it in 1937, and it has since been generalized to arbitrary number fields and to more general cubic equations.