A076329 Numbers k for which rank of the elliptic curve y^2=x^3+k*x is 2.

14, 33, 34, 39, 46, 55, 63, 65, 66, 68, 73, 89, 94, 99, 105, 113, 114, 129, 138, 145, 150, 154, 155, 158, 178, 183, 185, 201, 203, 206, 209, 219, 224, 226, 233, 238, 254, 258, 260, 273, 274, 281, 289, 295, 299, 308, 310, 333, 334, 337, 345, 353, 354, 360, 385, 386, 388

Offset: 1

Author

N. J. A. Sloane, Nov 06 2002

Keywords

• nonn

References

• D. S. Jandu, Elliptic Curve, Infinite Bandwidth Publishing, N. Hollywood CA 2007.
• D. S. Jandu, Birch And Swinnerton Dyer Conjecture, Infinite Bandwidth Publishing, N. Hollywood CA 2007.
• D. Zagier & G. Harder, "La conjecture de Birch et Swinnerton-Dyer" in Les Dossiers de La Recherche, pp. 48-53 No. 20 August-October 2005 Paris.

Links

• B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves, I, J. Reine Angew. Math., 212 (1963), 7-25.
• A. L. Robledo, PlanetMath.org, Birch and Swinnerton-Dyer conjecture
• W. A. Stein, The Birch and Swinnerton-Dyer Conjecture, Part 1
• W. A. Stein, The Birch and Swinnerton-Dyer Conjecture, Part 2
• W. A. Stein, The Birch and Swinnerton-Dyer Conjecture, Part 3
• Wikipedia, Birch and Swinnerton-Dyer conjecture

Crossrefs

Cf. A002150-A002159.

Programs

PARI

for(k=1, 1e3, if(ellanalyticrank(ellinit([0, 0, 0, k, 0]))[1]==2, print1(k", "))) \\ Seiichi Manyama, Jul 07 2019

Extensions

More terms added by Seiichi Manyama, Jul 07 2019