Détermination de courbes elliptiques pour la conjecture de Szpiro, by Abderrahmane Nitaj

This paper has appeared in Acta Arith. 85 (1998), no.4, 351-376, and so the dvi version has been removed. Let E/Q be an elliptic curve with minimal discriminant D and conductor N. A conjecture of Szpiro asserts that the ratio s=s(E)=log |D|/log N is bounded and its asymptotic value is 6. We describe several methods which permit us to search for elliptic curves having a relatively high ratio s. Using parametric families of elliptic curves, we also give several tables of individual examples of curves having the highest ratio s currently known.

Abderrahmane Nitaj <nitaj@diana.math.uni-sb.de>