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%I #11 Mar 19 2019 12:54:18
%S 1254,2605,2774,3502,4199,4669,4895,6286,6671,7230,7766,8005,9015,
%T 9430,9654,10199,10549,11005,11029,12166,12270,12534,12935,13317,
%U 14965,15655,16151,16206,16887,17958,18221,19046,19726,20005,20366
%N Squarefree n such that the elliptic curve n*y^2 = x^3 - x arising in the "congruent number" problem has rank 3.
%C Conjectural, as detailed in the pages from which it is extracted (see the first few links at the web site mentioned for details), but the conjecture is supported by much numerical and theoretical evidence.
%H A. Dujella, A. S.Janfeda, S. Salami, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Janfada/janfada3.html">A Search for High Rank Congruent Number Elliptic Curves</a>, JIS 12 (2009) 09.5.8.
%H N. D. Elkies, <a href="http://www.math.harvard.edu/~elkies/compnt.html">Algorithmic (a.k.a. Computational) Number Theory: Tables, Links, etc.</a>
%H Fidel Ronquillo Nemenzo, <a href="https://doi.org/10.3792/pjaa.74.29">All congruent numbers less than 40000</a>, Proc. Japan Acad. Ser. A Math. Sci., Volume 74, Number 1 (1998), 29-31. See Table IV p. 31.
%o (PARI) r(n)=ellanalyticrank(ellinit([0,0,0,-n^2,0]))[1]
%o for(n=1,1e4,if(r(n)==3,print1(n", "))) \\ _Charles R Greathouse IV_, Sep 01 2011
%Y Cf. A062694, A062695.
%K nonn
%O 0,1
%A _Noam D. Elkies_, Jul 04 2001