Israel Journal of Mathematics

, Volume 85, Issue 1–3, pp 79–83

Curves with infinitely many points of fixed degree


DOI: 10.1007/BF02758637

Cite this article as:
Frey, G. Israel J. Math. (1994) 85: 79. doi:10.1007/BF02758637


Thed-th symmetric productC(d) of a curveC defined over a fieldK is closely related to the set of points ofC of degree ≤d. IfK is a number field, then a conjecture of Lang [Hi] proved by Faltings [Fa2] implies ifC(d)(K) is an infinite set, then there is aK-rational covering ofC → ℙ|K1 of degree ≤2d. As an application one gets that for fixed fieldK and fixedd there are only finitely many primes ι such that the set of all elliptic curves defined over some extensionsL ofK with [LK]≤d and withL-rational isogeny of degree ι is infinite.

Copyright information

© Hebrew University 1994

Authors and Affiliations

  1. 1.Institut für Experimentelle MathematikUniversität GH EssenEssen 12Germany

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