摘要
For elliptic curves the rank is one of the most essential numerical charactenstics. By means of finding the independent generators of the rational points on such a curve one may determine the lower bound of the rank. In this note we obtain a formula for the rank of elliptic curves defined over the rational numbers. Moreover, if we admit a conjecture suggested by S. Lang, then the proof of our formula provides an algorithm for calculating the rank.
基金
Project supported by the National Natural Science Foundation (Tianvuan Funds) of China.
