Computations of the rank of elliptic curve \(y^ 2=x^ 3-n^ 2x\) (Q1340361)

In this paper the rank of the elliptic curve \(y^ 2 = x^ 3 - n^ 2x\) \((n\) is a square free integer) for \(n < 1000\), and the order of the Hasse-Weil function, for \(n < 30000\), are computed. For this purpose, the authors utilize programs written in UBASIC that apply the methods given by \textit{J. S. Chahal} in ``Topics in number theory'' [Univ. Ser. Math. (New York 1988; Zbl 0711.11001)], and by \textit{J. E. Cremona} in ``Algorithms for modular elliptic curves'' (Cambridge 1992; Zbl 0758.14042).