
We use an invarianttheoretic method to compute certain twists of the modular curves X(n) for n = 7,9,11. 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 show by giving explicit nontrivial examples over Q(T) that there are infinitely many examples over Q in the cases n = 9 and n = 11.