Sur le rang des courbes elliptiques sur les corps de classes de Hilbert

Abstract

AbstractLet E/ℚ be an elliptic curve and let D<0 be a sufficiently large fundamental discriminant. If $E(\overline {\BmQ })$ contains Heegner points of discriminant D, those points generate a subgroup of rank at least |D|δ, where δ>0 is an absolute constant. This result is compatible with the Birch and Swinnerton-Dyer conjecture.