Geodesic
On families of 9-congruent elliptic curves
Tom Fisher1
1 DPMMS, Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WB, UK
Acta Arithmetica, Tome 171 (2015) no. 4, pp. 371-387.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 ${\mathbb Q}$, i.e. pairs of non-isogenous elliptic curves over ${\mathbb Q}$ whose $9$-torsion subgroups are isomorphic as Galois modules.
DOI : 10.4064/aa171-4-5
Keywords: compute equations families elliptic curves congruent given elliptic curve these infinitely many non trivial pairs congruent elliptic curves mathbb pairs non isogenous elliptic curves mathbb whose torsion subgroups isomorphic galois modules

Tom Fisher 1

1 DPMMS, Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WB, UK 
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Tom Fisher. On families of 9-congruent elliptic curves. Acta Arithmetica, Tome 171 (2015) no. 4, pp. 371-387. doi : 10.4064/aa171-4-5. http://geodesic.mathdoc.fr/articles/10.4064/aa171-4-5/

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