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

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

Author

N. J. A. Sloane

Keywords

• nonn

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, web.archive.org copy of the "MORDELL+" file on the SIMATH web site shut down in 2017. [Locally cached copy].
• H. Mishima, Tables of Elliptic Curves.

Crossrefs

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

Programs

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

Extensions

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