|
%I M4782 N2040 #32 Oct 14 2023 23:49:16
%S 11,26,39,47,53,61,67,76,83,89,104,106,109,116,118,121,139,147,152,
%T 155,170,186,191,200,207,211,212,214,219,222,233,236,244,249,262,277,
%U 286,291,293,294,298,299,327,329,334,355,356,364,366,368,370,371,391,393,397
%N Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 2.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H B. J. Birch and H. P. F. Swinnerton-Dyer, <a href="https://doi.org/10.1515/crll.1963.212.7">Notes on elliptic curves, I</a>, J. Reine Angew. Math., 212 (1963), 7-25.
%o (PARI) for(k=1, 1e3, if(ellanalyticrank(ellinit([0, 0, 0, 0, -k]))[1]==2, print1(k", "))) \\ _Seiichi Manyama_, Jul 06 2019
%o (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
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E Better definition from _Artur Jasinski_, Jun 30 2010
%E More terms added by _Seiichi Manyama_, Jul 06 2019
|
