Note on equality of L-functions of elliptic curves

Abstract.

We study the equality L (A,K,s) = L (B,M,s) where A,B are elliptic curves defined over ${\Bbb Q}$, and K,M Galois number fields. Using Faltings theorem on isogenies of abelian varieties, Serre theorem on supersingular reduction of elliptic curves and properties of Weil functor of restriction of scalars, the equality is described completely.