A002154 Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 2.

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

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.

Programs

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

PARI

for(k=1, 1e3, if(ellanalyticrank(ellinit([0, 0, 0, 0, -k]))[1]==2, 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