This poster describes Lenstra’s Elliptic Curve Algorithm for factoring large numbers. The authors starts from the definition of elliptic curves over fields of characteristic different than 2 or 3. Then he introduces a construction of the abelian group over the K-rational points of an elliptic curve. Next he reminds Pollard’s p − 1 algorithm and introduces Lenstra's Algorithm. This poster discusses how Lenstra’s improves upon Pollard and it gives a brief note on application.