

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
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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. SwinnertonDyer, Notes on elliptic curves, I, J. Reine Angew. Math., 212 (1963), 725.
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, A060951A060953.
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



