Computing the number of points on an elliptic curve over a finite field: algorithmic aspects
The author describes in some detail his implementation of Schoof's algorithm to compute the number of rational points on an elliptic curve over a prime field. His algorithm depends on the practical improvements of Atkin and Elkies. The author explains how to compute convenient equations of certain modular curves and how to find factors of the division polynomials. He illustrates his efficient program by computing the number of points on an elliptic curve modulo the 500 digit prime \(p= 10^{499}+ 153\).
scientific article; zbMATH DE number 858027