A002151 Numbers k for which rank of the elliptic curve y^2 = x^3 + k is 0. (Formerly M3271 N1321)

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

1,2

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.

Prog

(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

Crossrefs

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

Sequence in context: A302165 A102144 A102138 * A276931 A192046 A286488

Adjacent sequences: A002148 A002149 A002150 * A002152 A002153 A002154

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

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

Status

approved