A102833 Numbers n for which rank of the elliptic curve y^2=x^3+n is 3.

113, 141, 316, 346, 359, 427, 443, 506, 537, 568, 659, 681, 730, 745, 873, 892, 899, 940, 997, 1016, 1025, 1090, 1149, 1157, 1171, 1213, 1304, 1305, 1342, 1367, 1373, 1478, 1522, 1639, 1646, 1737, 1753, 1772, 1811, 1841, 1897, 1907, 1954, 2024, 2143

Offset: 1

Author

James R. Buddenhagen, Feb 18 2005. Entry revised by N. J. A. Sloane, Jun 10 2012

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n=1..250 (using Gebel).
• B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves, I, J. Reine Angew. Math., 212 (1963), 7-25.
• J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
• H. Mishima, Tables of Elliptic Curves

Crossrefs

Cf. A060950, A002151, A002153, A002155, A060748, A060838, A060951-A060953.

Programs

Magma

for k in[1..2000] do if Rank(EllipticCurve([0,0,0,0,k])) eq 3 then print k; end if; end for; // Vaclav Kotesovec, Jul 07 2019

Extensions

More terms from T. D. Noe, Jul 24 2007