Abstract
Mazur and Rubin introduced the notion of n-Selmer companion elliptic curves and gave several examples of pairs of non-isogenous Selmer companions. We construct several pairs of families of elliptic curves, each parameterised by t ∈ Z , such that the two curves in a pair corresponding to a given t are non-isogenous 3-Selmer companions, possibly provided that t satisfies a simple congruence condition.