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 A062695 Squarefree n such that the elliptic curve n*y^2 = x^3 - x arising in the "congruent number" problem has rank 2. 16
 34, 41, 65, 137, 138, 145, 154, 161, 194, 210, 219, 226, 257, 265, 291, 299, 313, 323, 330, 353, 371, 386, 395, 410, 426, 434, 442, 457, 465, 505, 514, 546, 561, 602, 609, 651, 658 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS A. Dujella, A. S. Janfeda, S. Salami, A Search for High Rank Congruent Number Elliptic Curves, JIS 12 (2009) 09.5.8 G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340. G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy] Kazunari Noda and Hideo Wada, All congruent numbers less than 10000, Proc. Japan Acad. Ser. A Math. Sci., Volume 69, Number 6 (1993), 175-178. PROG (PARI) r(n)=ellanalyticrank(ellinit([0, 0, 0, -n^2, 0]))[1] 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 CROSSREFS Cf. A003273, A006991, A062693, A062694, A259680-A259687. Sequence in context: A296096 A045044 A108303 * A107730 A320703 A095419 Adjacent sequences:  A062692 A062693 A062694 * A062696 A062697 A062698 KEYWORD nonn AUTHOR Noam D. Elkies, Jul 04 2001 STATUS approved

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Last modified June 20 17:51 EDT 2019. Contains 324234 sequences. (Running on oeis4.)