A062693 Squarefree n such that the elliptic curve n*y^2 = x^3 - x arising in the "congruent number" problem has rank 3.

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

Table of n, a(n) for n=0..34.

A. Dujella, A. S.Janfeda, S. Salami, A Search for High Rank Congruent Number Elliptic Curves, JIS 12 (2009) 09.5.8.

N. D. Elkies, Algorithmic (a.k.a. Computational) Number Theory: Tables, Links, etc.

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

Cf. A062694, A062695.

Sequence in context: A252157 A252150 A023068 * A067203 A230544 A280928

Adjacent sequences: A062690 A062691 A062692 * A062694 A062695 A062696

Keyword

nonn

Author

Noam D. Elkies, Jul 04 2001

Status

approved