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

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

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

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

Crossrefs

Cf. A002152 (rank 1), A002154 (rank 2), A179136 (rank 3), A179137 (rank 4).

Cf. A060951.

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

PARI

for(k=1, 200, if(ellanalyticrank(ellinit([0, 0, 0, 0, -k]))[1]==0, print1(k", "))) \\ Seiichi Manyama, Jul 06 2019

Extensions

Better definition from Artur Jasinski, Jun 30 2010

More terms added by Seiichi Manyama, Jul 06 2019