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arXiv · 1306.0027

Elliptic curves with torsion group Z/8Z or Z/2Z x Z/6Z

Andrej Dujella·Juan Carlos Peral
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Abstract

We show the existence of families of elliptic curves over Q whose generic rank is at least 2 for the torsion groups Z/8Z and Z/2Z x Z/6Z. Also in both cases we prove the existence of infinitely many elliptic curves, which are parameterized by the points of an elliptic curve with positive rank, with such torsion group and rank at least 3. These results represent an improvement of previous results by Campbell, Kulesz, Lecacheux, Dujella and Rabarison where families with rank at least 1 were constructed in both cases.

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Andrej Dujella, Juan Carlos Peral. 2013-05-31. Elliptic curves with torsion group Z/8Z or Z/2Z x Z/6Z. https://doi.org/10.1090/conm%2F649

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