login
A002151
Numbers k for which rank of the elliptic curve y^2 = x^3 + k is 0.
(Formerly M3271 N1321)
13
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]
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
KEYWORD
nonn
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