The local root number of elliptic curves with wild ramification

Let E be an elliptic curve over a number field F. The root number is conjecturally the sign of the functional equation of L-function of E/F. It is defined as the product of local signs over all places of F. The purpose of this paper is to describe this local sign by the coefficients of a Weierstra? equation of E. Received: 31 March 2000 / Revised version: 22 November 2001 / Published online: 23 May 2002