Elliptic Curves of Large Rank and Small Conductor

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Elliptic Curves of Large Rank and Small Conductor

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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.
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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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  • FAS Scholarly Articles [7594]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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