Minoration du rang des courbes elliptiques sur les corps de classes de Hilbert

Abstract

Soit $E/\BmQ$ une courbe elliptique. Soit $D<0$ un discriminant fondamental suffisamment grand. Si $E(\bar{\BmQ})$ contient des points de Heegner de discriminant $D$, ces points engendrent un sous-groupe dont le rang est supérieur à $\pabs{D}^{0.0009}$. Ce résultat est en accord avec la conjecture de Birch et Swinnerton-Dyer. --- Let $E/\BmQ$ be an elliptic curve. Let $D<0$ be a sufficiently large fundamental discriminant. If $E(\bar{\BmQ})$ contains Heegner points of discriminant $D$, these points generate a subgroup of rank greater than $\pabs{D}^{0.0009}$. This result is in agreement with the conjecture of Birch and Swinnerton-Dyer.

short version to appear in Compositio

References in corpus (2)

• The subconvexity problem for $\GL_{2}$
• Heegner points and Eisenstein series

Cited by in corpus (2)

• Mordell-Weil growth for GL2-type abelian varieties over Hilbert class fields of CM fields
• Non-split Sums of Coefficients of GL(2)-Automorphic Forms