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. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Nagell-Lutz theorem (Wikipedia)
Statement of the theoremQuote, Statement of the theorem
If P = (x,y) is a rational point of finite order on E, for the elliptic curve group law, then:
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