On families of 9-congruent elliptic curves
Tom Fisher
Acta Arithmetica, Tome 168 (2015), p. 371-387 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:279340 
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     title = {On families of 9-congruent elliptic curves},
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     pages = {371-387},
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Tom Fisher. On families of 9-congruent elliptic curves. Acta Arithmetica, Tome 168 (2015) pp. 371-387. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-4-5/