Elliptic curves of large rank and small conductor

Details Elliptic curves of large rank and small conductor Elliptic curves of large rank and small conductor

2004-03-22

arxiv.org/abs/math/0403374v3

Mathematics

Number Theory

16 pages, including tables and one .eps figure; to appear in the Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised so

Scientific paper

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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