Journal Article10.1016/S0764-4442(99)80469-8
Sur le nombre de points de torsion rationnels sur une courbe elliptique
Marc Hindry,Joseph H. Silverman +1 more
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TL;DR: The authors prouvons que, for une courbe elliptique ayant bonne reduction partout, le nombre de points de torsion rationnels sur un corps de nombres est borne polynomialement en fonction du degre du corps de Nombres.
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Abstract: Resume Nous prouvons que, pour une courbe elliptique ayant bonne reduction partout, le nombre de points de torsion rationnels sur un corps de nombres est borne polynomialement en fonction du degre du corps de nombres. Ceci repond a une question de Flexor et Oesterle.
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Citations
Local Bounds for Torsion Points on Abelian Varieties
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A lower bound for average values of dynamical Green’s functions
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Lower bounds for the canonical height on elliptic curves over abelian extensions
TL;DR: In this article, it was shown that if E has non-integral j-invariant (i.e., it does not have complex multiplication) points, then there is a lower bound for the canonical height of non-torsion points on E defined over the maximal abelian extension of K of E/K.
30
Global discrepancy and small points on elliptic curves
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TL;DR: In this paper, the authors define the "global discrepancy" of a finite set Z ⊂ E(k), which measures how far the set is from being adelically equidistributed.
29
References
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The Arithmetic of Elliptic Curves
Joseph H. Silverman
- 01 Jan 1986
TL;DR: It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.
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Advanced Topics in the Arithmetic of Elliptic Curves
Joseph H. Silverman
- 01 Jan 1994
TL;DR: In this article, the authors continue the study of elliptic curves by presenting six important, but somewhat more specialized topics: Elliptic and modular functions for the full modular group.
2.2K
Modular curves and the Eisenstein ideal
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Bornes pour la torsion des courbes elliptiques sur les corps de nombres
TL;DR: In this paper, Weil showed that for a Courbe elliptique E, the point de torsion of E(K) soit d'ordre ≤ B(d).
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