  Let O_K be a discrete valuation ring with field of fractions K and perfect
residue field. Let E be an elliptic curve over K, let L/K be a finite Galois
extension and let O_L be the integral closure of O_K in L. Denote by X' the
minimal regular model of E_L over O_L. We show that the special fibers of the
minimal Weierstrass model and the minimal regular model of E over O_K are
determined by the infinitesimal fiber X'_m together with the action of
Gal(L/K), when m is big enough (depending on the minimal discriminant of E and
the different of L/K).
