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A062693
Squarefree n such that the elliptic curve n*y^2 = x^3 - x arising in the "congruent number" problem has rank 3.
4
1254, 2605, 2774, 3502, 4199, 4669, 4895, 6286, 6671, 7230, 7766, 8005, 9015, 9430, 9654, 10199, 10549, 11005, 11029, 12166, 12270, 12534, 12935, 13317, 14965, 15655, 16151, 16206, 16887, 17958, 18221, 19046, 19726, 20005, 20366
OFFSET
0,1
COMMENTS
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.
LINKS
A. Dujella, A. S.Janfeda, S. Salami, A Search for High Rank Congruent Number Elliptic Curves, JIS 12 (2009) 09.5.8.
Fidel Ronquillo Nemenzo, All congruent numbers less than 40000, Proc. Japan Acad. Ser. A Math. Sci., Volume 74, Number 1 (1998), 29-31. See Table IV p. 31.
PROG
(PARI) r(n)=ellanalyticrank(ellinit([0, 0, 0, -n^2, 0]))[1]
for(n=1, 1e4, if(r(n)==3, print1(n", "))) \\ Charles R Greathouse IV, Sep 01 2011
CROSSREFS
Sequence in context: A252157 A252150 A023068 * A067203 A230544 A280928
KEYWORD
nonn
AUTHOR
Noam D. Elkies, Jul 04 2001
STATUS
approved