The Lenstra elliptic-curve factorization algorithm is a method used to find nontrivial factors of large integers. It leverages the properties of elliptic curves over finite fields, making it efficient for numbers with small factors. The algorithm is particularly effective when the integer to be factored has a prime factor that is relatively small compared to the number itself. This algorithm operates by selecting a random elliptic curve and a point on it, then using mathematical operations to find a factor of the integer. Its performance is generally better than traditional methods like Pollard's rho algorithm for certain types of numbers, especially those with small prime factors.