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Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 1.
(Formerly M2429 N0962)
9

%I M2429 N0962 #32 Oct 14 2023 16:01:22

%S 3,5,8,9,13,15,18,19,20,21,24,28,29,31,35,37,40,47,48,49,51,53,56,60,

%T 61,67,69,77,79,80,83,84,85,88,90,92,93,95,98,100,101,104,109,111,115,

%U 120,121,124,125,126,127,128,131,133,136,141,143,144,148,149,152,153,156

%N Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 1.

%C Terms 80 and 128 are missing in the article by Birch and Swinnerton-Dyer, page 25, table 4b. - _Vaclav Kotesovec_, Jul 07 2019

%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="/A002159/b002159.txt">Table of n, a(n) for n = 1..2040</a>

%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.

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

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

%Y Cf. A060953, A076329.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms added by _Seiichi Manyama_, Jul 07 2019