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We give an algorithm that, given an elliptic curve $E$ over $\Qbar$ inWeierstra{\ss} form, computes the infimum and supremum of the differencebetween the na\"{\i}ve and canonical height functions on $E(\Qbar)$.  Nousdonnons un algorithme qui, \'etant donn\'ee une courbe elliptique $E$ sur$\Qbar$ sous la forme de Weierstra\ss, calcule l'infimum et le supremum de ladiff\'erence entre la hauteur na\"{\i}ve et la hauteur canonique sur$E(\Qbar)$.

Bornes optimales pour la diff\'erence entre la hauteur de Weil et la hauteur de N\'eron-Tate sur les courbes elliptiques sur \Qbar