The Elliptic Curve Method (ECM) is an algorithm used for integer factorization, which is the process of breaking down a composite number into its prime factors. It leverages the mathematical properties of elliptic curves, which are smooth, projective algebraic curves defined by cubic equations. ECM is particularly effective for finding small factors of large numbers. In ECM, points on an elliptic curve are used to perform arithmetic operations, which helps in identifying factors. The method is efficient for numbers with small prime factors and is often used in cryptography, where the security of systems like RSA relies on the difficulty of factorization.