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Rank of elliptic curve y^2 = x^3 + n*x.
15

%I #29 Jul 10 2019 04:05:52

%S 0,0,1,0,1,0,0,1,1,0,0,0,1,2,1,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,2,2,

%T 1,0,1,0,2,1,0,0,0,0,0,2,1,1,1,0,1,0,1,0,2,1,0,0,0,1,1,0,2,0,2,2,1,2,

%U 1,0,0,0,2,0,0,0,1,0,1,1,0,0,1,1,1,0,0,1,2,1,0,1,1,2,1,0,0,1,2,1,1,0,0,1,2

%N Rank of elliptic curve y^2 = x^3 + n*x.

%H Seiichi Manyama, <a href="/A060953/b060953.txt">Table of n, a(n) for n = 1..1000</a>

%H H. Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/ec/eca1/ec02rp.txt">Tables of Elliptic Curves</a>

%H F. Richman, <a href="http://math.fau.edu/Richman/elliptic.htm">Elliptic curves</a>

%H K. Rubin and A. Silverberg, <a href="http://www.ams.org/bull/2002-39-04/S0273-0979-02-00952-7/home.html">Ranks of elliptic curves</a>

%F a(-n) = A060952(n). - _Michael Somos_, Dec 15 2011

%o (PARI) { A060953(n) = ellanalyticrank( ellinit([0,0,0,n,0]) )[1]; }

%Y Cf. A060748, A060838, A060950-A060953.

%K nonn,nice

%O 1,14

%A _N. J. A. Sloane_, May 10 2001

%E Lambert Klasen (Lambert.Klasen(AT)gmx.net), Mar 31 2005, kindly rechecked this sequence against the Mishima web site and found no errors.

%E Corrected Apr 10 2005 at the suggestion of _James R. Buddenhagen_. There were errors caused by the fact that Mishima lists each curve of rank two twice, once for each generator.

%E Extended by _Max Alekseyev_, Mar 09 2009