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arXiv · 1503.08378

Collinear CM-points

Yuri Bilu·Florian Luca·David Masser
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Abstract

André's celebrated Theorem of 1998 implies that each complex straight line (apart from obvious exceptions) contains at most finitely many points whose both coordinates are j-invariants of elliptic curves with complex multiplication. We show that there are only a finite number of such lines which contain more than two such points. As there is a line through any two complex points, this is best possible.

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Yuri Bilu, Florian Luca, David Masser. 2016-11-28. Collinear CM-points. https://doi.org/10.2140/ant.2017.11.1047

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