Effective bounds for the torsion of elliptic curves over number fields. (Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres.) (French) Zbl 0919.11040

Parent, Pierre

J. Reine Angew. Math. 506, 85-116 (1999).

Let \(E\) be an elliptic curve over a number field \(K\) which is of degree \(d\) over \(\mathbb{Q}\). The theorem of Mazur-Kamienny-Merel asserts that there exists an integer \(B(d)\), depending only on \(d\), such that the torsion subgroups of the \(k\)-rational points of \(E\) has order less than \(B(d)\); but their bounds were not effective. In this paper we give explicit expressions for \(B(d)\).

Reviewer: P.Parent (Rennes)

MSC:

11G05	Elliptic curves over global fields
14H52	Elliptic curves

Keywords:

order of the torsion subgroup of the \(k\)-rational points; effective bounds; elliptic curve