## 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

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
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