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

Author

Noam D. Elkies, Jul 04 2001

Keywords

• nonn

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.
• 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.

Crossrefs

Cf. A062694, A062695.

Programs

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