A002150 Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 0. (Formerly M2391 N0949)

1, 3, 5, 6, 8, 9, 10, 12, 14, 16, 17, 24, 27, 31, 32, 33, 34, 36, 37, 41, 42, 46, 52, 62, 64, 68, 69, 70, 73, 77, 78, 80, 82, 86, 88, 90, 92, 96, 97, 98, 99, 103, 105, 108, 111, 113, 114, 117, 119, 122, 125, 132, 133, 134, 136, 141, 142, 144, 145, 149, 154, 156, 158, 160

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

Table of n, a(n) for n=1..64.

B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves, I, J. Reine Angew. Math., 212 (1963), 7-25.

Prog

(PARI) for(k=1, 200, if(ellanalyticrank(ellinit([0, 0, 0, 0, -k]))[1]==0, print1(k", "))) \\ Seiichi Manyama, Jul 06 2019
(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. A002152 (rank 1), A002154 (rank 2), A179136 (rank 3), A179137 (rank 4).

Cf. A060951.

Sequence in context: A165290 A307206 A026430 * A153264 A249595 A133561

Adjacent sequences: A002147 A002148 A002149 * A002151 A002152 A002153

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Better definition from Artur Jasinski, Jun 30 2010

More terms added by Seiichi Manyama, Jul 06 2019

Status

approved