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Indivisible Points on Families of Elliptic Curves

✍ Scribed by Rajiv Gupta; Keith Ramsay

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 376 KB
Volume: 63
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1997.2092

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✦ Synopsis

In this paper we consider families of elliptic curves E n over Q arising as twists. Given rational points P n on E n , we ask how often P n is indivisible in the group of rational points of E n , as n varies over the positive integers. We prove, following the method of Silverman for families with non-constant j-invariant, that, under mild restrictions, P n is indivisible almost always, in a density sense. We also prove in certain cases that, for a fixed m, the point P n is divisible by m for only finitely many n.

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