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Numbers k for which the rank of the elliptic curve y^2 = x^3 + k is 1.
(Formerly M0682 N0251)
12

%I M0682 N0251 #34 Jul 06 2024 12:02:28

%S 2,3,5,8,9,10,11,12,18,19,22,26,28,30,31,33,35,36,38,39,40,41,44,46,

%T 47,48,50,52,54,55,56,58,61,62,66,67,68,69,71,72,74,76,77,80,82,83,91,

%U 92,94,97,98,99,100,102,103,105,107,108,110,111,112,117,118,119

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

%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 T. D. Noe, <a href="/A002153/b002153.txt">Table of n, a(n) for n = 1..5111</a> (using Gebel).

%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 J. Gebel, <a href="https://web.archive.org/web/20160825170558/http://tnt.math.se.tmu.ac.jp/simath/MORDELL/MORDELL+">Integer points on Mordell curves</a>, web.archive.org copy of the "MORDELL+" file on the SIMATH web site shut down in 2017. <a href="/A001014/a001014_2.txt">[Locally cached copy]</a>.

%H H. Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/ec/eca1/ec01rp.txt">Tables of Elliptic Curves</a>.

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

%Y Cf. A060950, A002151, A002155, A102833, A060748, A060838, A060951-A060953.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E Corrected and extended by _James R. Buddenhagen_, Feb 18 2005