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) 
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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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