Signes locaux des courbes elliptiques en 2 et 3

Abstract

Let p be a prime number. Associated to every elliptic curve E over Q p there is a local root number W p(E) = ±1, constructed from the local epsilon factors of Deligne. This sign is already known when p > 3, and also, in certain cases, when p = 2 or 3. In this Note, we give the value of W 2 or W 3 in all cases. Concerning W 3, for our results to be valid, we have to assume that a certain (finite) number of auxiliary elliptic curves over Q are Weil curves.