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.

1, 2, 11, 113, 2089, 28279, 975379

Offset: 0

Author

N. J. A. Sloane, Jul 04 2024

Keywords

• nonn
• more
• hard

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

Cf. A031507, A031508, A081119.