An algorithm for the rank of elliptic curves
An asymptotic formula for the rank \(r\) of an elliptic curve \(E\) over the rationals \(\mathbb{Q}\) is given and a conjecture of \(S\). Lang on the size of the Néron-Tate height of basis points of the Mordell-Weil group \(E (\mathbb{Q})\) is claimed to lead to an algorithm for determining \(r\) provided Lang's conjecture is true and the constants involved can be effectively computed. No proofs are given. We mention that an algorithm for computing the rank \(r\) and a basis of the group \(E(\mathbb{Q})\), based on ideas of Manin and assuming the truth of the conjectures of Birch and Swinnerton-Dyer was developed by \textit{J. Gebel} and the reviewer [in Elliptic curves and related topics, CRM Proc. Lect. Notes 4, 61-83 (1994)].
Néron-Tate height of basis points of the Mordell-Weil group
scientific article; zbMATH DE number 468822