Selmer companion curves
Abstract
We say that two elliptic curves E1, E2 over a number field K are n-Selmer companions for a positive integer n if for every quadratic character of K, there is an isomorphism between the n-Selmer groups Seln(E1/K) and Seln(E2/K) of the quadratic twists E1, E2. We give sufficient conditions for two elliptic curves to be n-Selmer companions, and give a number of examples of non-isogenous pairs of companions.
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