A002151 Numbers k for which rank of the elliptic curve y^2 = x^3 + k is 0.

1, 4, 6, 7, 13, 14, 16, 20, 21, 23, 25, 27, 29, 32, 34, 42, 45, 49, 51, 53, 59, 60, 64, 70, 75, 78, 81, 84, 85, 86, 87, 88, 90, 93, 95, 96, 104, 109, 114, 115, 116, 123, 124, 125, 135, 137, 140, 144, 153, 157, 158, 159, 160, 162, 165, 167, 173, 175, 176, 178

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..2907 (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]
• L. Lehman, Elliptic Curves of Rank Zero.
• H. Mishima, Tables of Elliptic Curves.

Crossrefs

Cf. A060950, A002153, A002155, A102833, A060748, A060838, A060951, A060952, A060953.

Programs

Magma

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

Extensions

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

The missing entry 123 was added by T. D. Noe, Jul 24 2007