# Six unlikely intersection problems in search of effectivity

Habegger, Philipp and Jones, Gareth and Masser, David. (2015) Six unlikely intersection problems in search of effectivity. Preprints Fachbereich Mathematik, 2015 (28).

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Official URL: https://edoc.unibas.ch/70007/

We investigate four properties related to an elliptic curve $E_t$ in Legendre form with parameter t: the curve $E_t$ has complex multiplication, $E_{-t}$ has complex multiplication, a point on $E_t$ 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. We solve these problems effectively and in certain cases also explicitly.