English

Six unlikely intersection problems in search of effectivity

Number Theory 2016-08-03 v1

Abstract

We investigate four properties related to an elliptic curve EtE_t in Legendre form with parameter tt: the curve EtE_{t} has complex multiplication, EtE_{-t} has complex multiplication, a point on EtE_t with abscissa 22 is of finite order, and tt 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.

Keywords

Cite

@article{arxiv.1509.06573,
  title  = {Six unlikely intersection problems in search of effectivity},
  author = {P. Habegger and G. Jones and D. Masser},
  journal= {arXiv preprint arXiv:1509.06573},
  year   = {2016}
}
R2 v1 2026-06-22T11:02:38.128Z