Algebraic Geometry Commons^™

On Elliptic Curves, Montana S. Miller

MSU Graduate Theses

An elliptic curve over the rational numbers is given by the equation y² = x³+Ax+B. In our thesis, we study elliptic curves. It is known that the set of rational points on the elliptic curve form a finitely generated abelian group induced by the secant-tangent addition law. We present an elementary proof of associativity using Maple. We also present a relatively concise proof of the Mordell-Weil Theorem.