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A052432
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Smallest conductor of elliptic curve with rank n.
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0
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OFFSET
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0,1
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COMMENTS
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The smallest known conductors for ranks 5, 6, 7, and 11 are 19047851, 5187563742, 382623908456, 18031737725935636520843, respectively. These are just upper bounds on a(n).
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LINKS
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EXAMPLE
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The curve "11a3": y^2 + y = x^3 - x^2 has rank 0.
The curve "37a1": y^2 + y = x^3 - x has rank 1 with generator [0, 0].
The curve "389a1": y^2 + y = x^3 + x^2 - 2 * x has rank 2 with generators [0, 0], [-1, 1].
The curve "5077a1": y^2 + y = x^3 - 7 * x + 6 has rank 3 with generators [0, 2], [-1, 3], [-2, 3]. (End)
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CROSSREFS
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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Jesper Petersen (u943254(AT)daimi.au.dk), Mar 14 2000
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EXTENSIONS
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Added value for rank 4 from Cremona's extended tables, by John Cremona, Apr 02 2012
Upper bounds for a(5)-a(7) and a(11) from Elkies & Watkins added by Jonathan Sondow, Oct 29 2013.
Unproved values for a(5)-a(7) and a(11) removed by N. J. A. Sloane, Jan 25 2016 at the suggestion of John Cremona.
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STATUS
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approved
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