对于定义在有理数 
上的椭圆曲线，有理点的群总是有限生成的（即，总是存在有限的群生成元集）。该定理由 Mordell (1922-23) 证明，并由 Weil (1928) 推广到数域上的阿贝尔簇。
Mordell-Weil 定理
参见
阿贝尔簇, 椭圆曲线使用 Wolfram|Alpha 探索
参考文献
Ireland, K. and Rosen, M. "The Mordell-Weil Theorem." Ch. 19 in A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, pp. 319-338, 1990.Mordell, L. J. "On the Rational Solutions of the Indeterminate Equations of the Third and Fourth Degrees." Proc. Cambridge Philos. Soc. 21, 179-192, 1922-23.Nagell, T. "Rational Points on Plane Algebraic Curves. Mordell's Theorem." §69 in Introduction to Number Theory. New York: Wiley, pp. 253-260, 1951.Serre, J. P. Lectures on the Mordell-Weil Theorem, 3rd ed. Braunschweig, Germany: Vieweg, 1997.Weil, A. "L'arithmétique sur les courbes algébriques." Acta Math. 52, 281-315, 1928.在 Wolfram|Alpha 中被引用
Mordell-Weil 定理引用为
Weisstein, Eric W. "Mordell-Weil Theorem." 来自 MathWorld--Wolfram 网络资源. https://mathworld.net.cn/Mordell-WeilTheorem.html