# Elliptic Curves of Large Rank and Small Conductor

 Title: Elliptic Curves of Large Rank and Small Conductor Author: Elkies, Noam; Watkins, Mark Note: Order does not necessarily reflect citation order of authors. Citation: Elkies, Noam D. and Mark Watkins. 2004. Elliptic curves of large rank and small conductor. Lecture Notes in Computer Science 3076: 42-56. Full Text & Related Files: Elkies - Elliptic curves of large rank.pdf (193.9Kb; PDF) Abstract: For $$r = 6, 7, . . . , 11$$ we find an elliptic curve $$E/Q$$ of rank at least $$r$$ and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for $$r = 6)$$ to over 100 (for $$r = 10$$ and $$r=11$$). We describe our search methods, and tabulate, for each $$r = 5, 6, . . . , 11$$, the five curves of lowest conductor, and (except for $$r = 11)$$ also the five of lowest absolute discriminant, that we found. Published Version: http://dx.doi.org/10.1007/b98210 Other Sources: http://arxiv.org/abs/math/0403374 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2958705

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Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University