Six unlikely intersection problems in search of effectivity

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We investigate four properties related to an elliptic curve Et in Legendre form with parameter t: the curve Et has complex multiplication, E−t has complex multiplication, a point on Et with abscissa 2 is of finite order, and t is a root of unity. Combining all pairs of properties leads to six problems on unlikely intersections. Using a variety of techniques we solve these problems with varying degrees of effectivity (and for three of them we even present the list of all possible t).

Bibliographical metadata

Original languageEnglish
JournalMathematical Proceedings of the Cambridge Philosophical Society
Early online date28 Jul 2016
StatePublished - 2016