Elliptic curves of large rank and small conductor

Noam D. Elkies; Mark Watkins

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Elliptic curves of large rank and small conductor

Noam D. Elkies·Mark Watkins

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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.

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Noam D. Elkies, Mark Watkins. 2004-05-11. Elliptic curves of large rank and small conductor. https://arxiv.org/abs/math/0403374

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