Mordell–Weil theorem
In mathematics, the Mordell–Weil theorem states that for an abelian variety A {\displaystyle A} over a number field K {\displaystyle K} , the group A ( K ) {\displaystyle A(K)} of K-rational points of A {\displaystyle A} is a finitely-generated abelian group, called the Mordell–Weil group. The case with A {\displaystyle A} an elliptic curve E {\displaystyle E} and K {\displaystyle K} the field of rational numbers is Mordell's theorem, answering a question apparently posed by Henri Poincaré around 1901; it was proven by Louis Mordell in 1922.