A002155 Numbers k for which the rank of the elliptic curve y^2 = x^3 + k is 2. (Formerly M4957 N2125)

15, 17, 24, 37, 43, 57, 63, 65, 73, 79, 89, 101, 106, 122, 129, 131, 142, 145, 148, 151, 161, 164, 168, 171, 186, 195, 197, 198, 204, 217, 222, 223, 225, 229, 232, 233, 248, 252, 260, 265, 268, 269, 281, 294, 295, 297, 303, 322, 331, 337, 347, 350, 353, 360, 366, 369, 373, 377, 381, 388, 389, 392, 404, 409, 412, 414, 433, 449, 464, 469, 481, 483, 485, 492

Offset

1,1

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..1724 (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]

L. Lehman, Elliptic Curves of Rank Two. [broken link]

H. Mishima, Tables of Elliptic Curves.

Prog

(Magma) for k in[1..500] do if Rank(EllipticCurve([0, 0, 0, 0, k])) eq 2 then print k; end if; end for; // Vaclav Kotesovec, Jul 07 2019

Crossrefs

Cf. A060950, A002151, A002153, A102833, A060748, A060838, A060951-A060953.

Sequence in context: A183981 A155111 A124334 * A290749 A091017 A157716

Adjacent sequences: A002152 A002153 A002154 * A002156 A002157 A002158

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from James R. Buddenhagen, Feb 18 2005

Status

approved