A002156 - OEIS

%I M2345 N0926 #34 Oct 14 2023 15:58:38

%S 1,3,4,8,9,11,13,16,18,19,24,27,28,29,33,35,40,43,44,48,51,59,61,63,

%T 64,67,68,75,81,83,88,91,92,93,98,100,104,107,108,109,113,115,120,121,

%U 123,125,126,128,129,131,139,144,152,153,157,163,164,168,172,173,176,177,179,180,187,189,193,195,198,200

%N Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 0.

%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 Vincenzo Librandi, <a href="/A002156/b002156.txt">Table of n, a(n) for n = 1..1730</a>

%H B. J. Birch and H. P. F. Swinnerton-Dyer, <a href="http://dx.doi.org/10.1515/crll.1963.212.7">Notes on elliptic curves, I</a>, J. Reine Angew. Math., 212 (1963), 7-25.

%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 (open access).

%o (Magma) for k in[1..200] do if Rank(EllipticCurve([0,0,0,-k,0])) eq 0 then print k; end if; end for; // _Vaclav Kotesovec_, Jul 07 2019

%o (PARI) for(k=1, 200, if(ellanalyticrank(ellinit([0, 0, 0, -k, 0]))[1]==0, print1(k", "))) \\ _Seiichi Manyama_, Jul 07 2019

%Y Cf. A060952.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E Corrected and extended by _Vaclav Kotesovec_, Jul 07 2019

%E New name by _Vaclav Kotesovec_, Jul 07 2019