Six unlikely intersection problems in search of effectivity

Abstract

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.

References in corpus (1)

• An explicit André-Oort type result for P^1(C) x G_m(C)

Cited by in corpus (2)

• Collinear CM-points
• Bound the difference of two singular moduli