In this talk I will describe a systematic investigation into congruences between the modptorsion modules ofelliptic curves defined overQ. For each such curveEand primepthep-torsionE[p] ofE, is a 2-dimensionalvector space overFpwhich carries a Galois action of the absolute Galois groupGQ. The structure of thisGQ-module is very well understood, thanks to the work of J.-P. Serre and others. When we say the twocurvesEandE′are ”congruent” we mean thatE[p] andE′[p] are isomorphic asGQ-modules. While suchcongruences are known to exist for all primes up to 17, the Frey-Mazur conjecture states thatpis bounded:more precisely, that there existsB >0 such that ifp > BandE[p] andE′[p] are isomorphic thenEandE′are isogenous. We report on work toward establishing such a bound for the elliptic curves in the LMFDBdatabase. Secondly, we describe methods for determining whether or not a given isomorphism betweenE[p]andE′[p] is symplectic (preserves the Weil pairing) or antisymplectic, and report on the results of applyingthese methods to the curves in the database.This is joint work with Nuno Freitas (Warwick).