KnowraMordell–Weil theoremLinked fromLinked fromThe 5 pages that link to Mordell–Weil theorem, each with the reason it gives.All 5Related 4Compared with 1Rational pointRelated: It gives a structural finiteness result for rational points on abelian varieties.Birch and Swinnerton-Dyer conjectureRelated: It makes the curve’s rational points a finitely generated group whose rank the conjecture predicts.Abelian varietyRelated: It makes rational points on abelian varieties accessible through finite generation.Arithmetic geometryRelated: It constrains the structure of rational points on elliptic curves and related varieties.Birch's theoremCompared with: It gives a structural result about rational points rather than an asymptotic count.