Author:
HABEGGER P.,JONES G.,MASSER D.
Abstract
AbstractWe 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).
Publisher
Cambridge University Press (CUP)
Reference40 articles.
1. An explicit Andre--Oort type result for $\mathbb{P}^1(\mathbb{C}) \times \mathbb{G}_m(\mathbb{C})$ based on logarithmic forms
2. Torsion points on families of squares of elliptic curves
3. EXPONENTIAL SUMS EQUATIONS AND THE SCHANUEL CONJECTURE
4. Y. André Shimura varieties, subvarieties, and CM points. Six lectures at the University of Hsinchu (Taiwan) (with an appendix by C.-L. Chai) http://math.cts.nthu.edu.tw/Mathematics/lecnotes/andre2001all.ps (2001).
5. A generalisation of the Chowla-Selberg formula;Nakkajima;J. Reine Angew. Math.,1991
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