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A373795
a(n) = smallest |k| such that the elliptic curve y^2 = x^3 + k has rank n, or -1 if no such k exists.
2
1, 2, 11, 113, 2089, 28279, 975379
OFFSET
0,2
COMMENTS
a(n) = min{ A031507(n), A031508(n) }.
See A031507 and A031508 for further information.
a(16) <= 1160221354461565256631205207888 (Elkies, ANTS-XVI, 2024). The same article also establishes the existence of a value of k which has rank >= 17. - N. J. A. Sloane, Jul 05 2024
REFERENCES
Noam D. Elkies, Rank of an elliptic curve and 3-rank of a quadratic field via the Burgess bounds, 2024 Algorithmic Number Theory Symposium, ANTS-XVI, MIT, July 2024.
LINKS
Noam D. Elkies and Zev Klagsbrun, New rank records for elliptic curves having rational torsion, ANTS XIV—Proceedings of the Fourteenth Algorithmic Number Theory Symposium, 233-250. Mathematical Sciences Publishers, Berkeley, CA, 2020.
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
N. J. A. Sloane, Jul 04 2024
STATUS
approved