A002153 Numbers k for which the rank of the elliptic curve y^2 = x^3 + k is 1. (Formerly M0682 N0251)

2, 3, 5, 8, 9, 10, 11, 12, 18, 19, 22, 26, 28, 30, 31, 33, 35, 36, 38, 39, 40, 41, 44, 46, 47, 48, 50, 52, 54, 55, 56, 58, 61, 62, 66, 67, 68, 69, 71, 72, 74, 76, 77, 80, 82, 83, 91, 92, 94, 97, 98, 99, 100, 102, 103, 105, 107, 108, 110, 111, 112, 117, 118, 119

Offset

1,1

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..5111 (using Gebel).

B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves, I, J. Reine Angew. Math., 212 (1963), 7-25.

J. Gebel, Integer points on Mordell curves. [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

H. Mishima, Tables of Elliptic Curves.

Prog

(Magma) for k in[1..200] do if Rank(EllipticCurve([0, 0, 0, 0, k])) eq 1 then print k; end if; end for; // Vaclav Kotesovec, Jul 07 2019

Crossrefs

Cf. A060950, A002151, A002155, A102833, A060748, A060838, A060951-A060953.

Sequence in context: A026260 A169655 A286489 * A047607 A113051 A047372

Adjacent sequences: A002150 A002151 A002152 * A002154 A002155 A002156

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Corrected and extended by James R. Buddenhagen, Feb 18 2005

Status

approved