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On families of 9-congruent elliptic curves

Tom 171 / 2015

Tom Fisher Acta Arithmetica 171 (2015), 371-387 MSC: 11G05, 11F80. DOI: 10.4064/aa171-4-5

Streszczenie

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.

Autorzy

  • Tom FisherDPMMS, Centre for Mathematical Sciences
    University of Cambridge
    Wilberforce Road
    Cambridge CB3 0WB, UK
    e-mail

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