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Soit $E/\BmQ$ une courbe elliptique. Soit $D<0$ un discriminant fondamentalsuffisamment grand. Si $E(\bar{\BmQ})$ contient des points de Heegner dediscriminant $D$, ces points engendrent un sous-groupe dont le rang estsup\'erieur \`a $\pabs{D}^{0.0009}$. Ce r\'esultat est en accord avec laconjecture de Birch et Swinnerton-Dyer.  ---  Let $E/\BmQ$ be an elliptic curve. Let $D<0$ be a sufficiently largefundamental discriminant. If $E(\bar{\BmQ})$ contains Heegner points ofdiscriminant $D$, these points generate a subgroup of rank greater than$\pabs{D}^{0.0009}$. This result is in agreement with the conjecture of Birchand Swinnerton-Dyer.

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