A002155 - OEIS

%I M4957 N2125 #35 Jul 06 2024 12:02:28

%S 15,17,24,37,43,57,63,65,73,79,89,101,106,122,129,131,142,145,148,151,

%T 161,164,168,171,186,195,197,198,204,217,222,223,225,229,232,233,248,

%U 252,260,265,268,269,281,294,295,297,303,322,331,337,347,350,353,360,366,369,373,377,381,388,389,392,404,409,412,414,433,449,464,469,481,483,485,492

%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 T. D. Noe, <a href="/A002155/b002155.txt">Table of n, a(n) for n = 1..1724</a> (using Gebel)

%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 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 L. Lehman, <a href="http://people.umw.edu/~llehman/ranktwo.htm">Elliptic Curves of Rank Two</a>. [broken link]

%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..500] do if Rank(EllipticCurve([0,0,0,0,k])) eq 2 then print k; end if; end for; // _Vaclav Kotesovec_, Jul 07 2019

%Y Cf. A060950, A002151, A002153, A102833, A060748, A060838, A060951-A060953.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _James R. Buddenhagen_, Feb 18 2005