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
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 <email@example.com>