|
%I #28 Oct 15 2023 14:21:38
%S 14,33,34,39,46,55,63,65,66,68,73,89,94,99,105,113,114,129,138,145,
%T 150,154,155,158,178,183,185,201,203,206,209,219,224,226,233,238,254,
%U 258,260,273,274,281,289,295,299,308,310,333,334,337,345,353,354,360,385,386,388
%N Numbers k for which rank of the elliptic curve y^2=x^3+k*x is 2.
%D D. S. Jandu, Elliptic Curve, Infinite Bandwidth Publishing, N. Hollywood CA 2007.
%D D. S. Jandu, Birch And Swinnerton Dyer Conjecture, Infinite Bandwidth Publishing, N. Hollywood CA 2007.
%D 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.
%H B. J. Birch and H. P. F. Swinnerton-Dyer, <a href="https://eudml.org/doc/150565">Notes on elliptic curves, I</a>, J. Reine Angew. Math., 212 (1963), 7-25.
%H A. L. Robledo, PlanetMath.org, <a href="http://planetmath.org/encyclopedia/BirchAndSwinnertonDyerConjecture.html">Birch and Swinnerton-Dyer conjecture</a>
%H W. A. Stein, <a href="http://wstein.org/edu/Fall2001/124/lectures/lecture34/lecture34">The Birch and Swinnerton-Dyer Conjecture, Part 1</a>
%H W. A. Stein, <a href="http://wstein.org/edu/Fall2001/124/lectures/lecture35/lecture35">The Birch and Swinnerton-Dyer Conjecture, Part 2</a>
%H W. A. Stein, <a href="http://wstein.org/edu/Fall2001/124/lectures/lecture36/lecture36">The Birch and Swinnerton-Dyer Conjecture, Part 3</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture">Birch and Swinnerton-Dyer conjecture</a>
%o (PARI) for(k=1, 1e3, if(ellanalyticrank(ellinit([0, 0, 0, k, 0]))[1]==2, print1(k", "))) \\ _Seiichi Manyama_, Jul 07 2019
%Y Cf. A002150-A002159.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Nov 06 2002
%E More terms added by _Seiichi Manyama_, Jul 07 2019
|
