
We use an invarianttheoretic method to compute certain twists of the modular curves X(n) for n = 7, 11. Searching for rational points on these twists enables us to find nontrivial pairs of ncongruent elliptic curves over Q, i.e. pairs of nonisogenous elliptic curves over Q whose ntorsion subgroups are isomorphic as Galois modules. We also find a nontrivial pair of 11congruent elliptic curves over Q(T), and hence give an explicit infinite family of nontrivial pairs of 11congruent elliptic curves over Q.