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On families of 9-congruent elliptic curves

We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over Q, i.e. pairs of non-isogenous elliptic curves over Q whose 9-torsion subgroups are isomorphic as Galois modules.

On families of 9-congruent elliptic curves   (18 pages)     dvi   ps   ps.gz   pdf
An earlier version of this paper, including similar results in the cases n = 7, 11, and accompanying electronic data, is available here.