Change of root numbers of elliptic curves under extension of scalars

In this paper we study how the root number attached to an elliptic curve E over a finite field extension K of Q3 changes when E is considered as an elliptic curve over a finite Galois extension F of K via extension of scalars. The main result is a formula relating the root number W(E/F) attached to E×KF to the root number W(E/K) attached to E.