Publication: Elliptic Curves of Large Rank and Small Conductor
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Date
2004
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Springer Verlag
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Elkies, Noam D. and Mark Watkins. 2004. Elliptic curves of large rank and small conductor. Lecture Notes in Computer Science 3076: 42-56.
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.
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