|
%I #30 Dec 12 2020 13:32:55
%S 34,41,65,137,138,145,154,161,194,210,219,226,257,265,291,299,313,323,
%T 330,353,371,386,395,410,426,434,442,457,465,505,514,546,561,602,609,
%U 651,658,674,689,721,723,731,761,777,793,866,889,890,905,915,985,987,995
%N Squarefree n such that the elliptic curve n*y^2 = x^3 - x arising in the "congruent number" problem has rank 2.
%C These n are precisely the primitive congruent numbers (A006991) with n==1, n==2, or n==3 (mod 8). - _T. D. Noe_, Aug 02 2006
%H Jinyuan Wang, <a href="/A062695/b062695.txt">Table of n, a(n) for n = 1..453</a>
%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 G. Kramarz, <a href="http://dx.doi.org/10.1007/BF01451411">All congruent numbers less than 2000</a>, Math. Annalen, 273 (1986), 337-340.
%H G. Kramarz, <a href="/A003273/a003273.pdf"> All congruent numbers less than 2000</a>, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]
%H Kazunari Noda and Hideo Wada, <a href="https://dx.doi.org/10.3792/pjaa.69.175">All congruent numbers less than 10000</a>, Proc. Japan Acad. Ser. A Math. Sci., Volume 69, Number 6 (1993), 175-178.
%o (PARI) r(n)=ellanalyticrank(ellinit([0,0,0,-n^2,0]))[1]
%o for(n=1,1e3,if(issquarefree(n)&&r(n)==2,print1(n", "))) \\ _Charles R Greathouse IV_, Sep 01 2011; corrected by _Frank M Jackson_, Aug 04 2016
%Y Cf. A003273, A006991, A062693, A062694, A259680-A259687.
%K nonn
%O 1,1
%A _Noam D. Elkies_, Jul 04 2001
%E More terms from _Jinyuan Wang_, Dec 12 2020
|
