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Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 0.
(Formerly M2391 N0949)
8

%I M2391 N0949 #35 Oct 14 2023 17:21:55

%S 1,3,5,6,8,9,10,12,14,16,17,24,27,31,32,33,34,36,37,41,42,46,52,62,64,

%T 68,69,70,73,77,78,80,82,86,88,90,92,96,97,98,99,103,105,108,111,113,

%U 114,117,119,122,125,132,133,134,136,141,142,144,145,149,154,156,158,160

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

%o (PARI) for(k=1, 200, if(ellanalyticrank(ellinit([0, 0, 0, 0, -k]))[1]==0, print1(k", "))) \\ _Seiichi Manyama_, Jul 06 2019

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

%Y Cf. A002152 (rank 1), A002154 (rank 2), A179136 (rank 3), A179137 (rank 4).

%Y Cf. A060951.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E Better definition from _Artur Jasinski_, Jun 30 2010

%E More terms added by _Seiichi Manyama_, Jul 06 2019