Six unlikely intersection problems in search of effectivity

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).

from # All Medicine by Alexandros G. Sfakianakis via alkiviadis.1961 on Inoreader http://ift.tt/2iKMRxS