A002154 Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 2. (Formerly M4782 N2040)

11, 26, 39, 47, 53, 61, 67, 76, 83, 89, 104, 106, 109, 116, 118, 121, 139, 147, 152, 155, 170, 186, 191, 200, 207, 211, 212, 214, 219, 222, 233, 236, 244, 249, 262, 277, 286, 291, 293, 294, 298, 299, 327, 329, 334, 355, 356, 364, 366, 368, 370, 371, 391, 393, 397

Offset

1,1

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..55.

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, 1e3, if(ellanalyticrank(ellinit([0, 0, 0, 0, -k]))[1]==2, print1(k", "))) \\ Seiichi Manyama, Jul 06 2019
(Magma) for k in[1..400] do if Rank(EllipticCurve([0, 0, 0, 0, -k])) eq 2 then print k; end if; end for; // Vaclav Kotesovec, Jul 07 2019

Crossrefs

Sequence in context: A329809 A190684 A354383 * A035934 A035932 A035933

Adjacent sequences: A002151 A002152 A002153 * A002155 A002156 A002157

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