A002158 Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 0. (Formerly M0981 N0369)

1, 2, 4, 6, 7, 10, 11, 12, 16, 17, 22, 23, 25, 26, 27, 30, 32, 36, 38, 41, 42, 43, 44, 45, 50, 52, 54, 57, 58, 59, 62, 64, 70, 71, 72, 74, 75, 76, 78, 81, 82, 86, 87, 91, 96, 97, 102, 103, 106, 107, 108, 110, 112, 116, 117, 118, 119, 122, 123, 130, 132, 134, 135, 137, 139, 140, 142, 146, 147, 151, 160, 161, 162, 166, 167, 169, 170, 172, 174, 176, 177, 182, 186, 187, 190, 192, 193, 194, 199

Offset

1,2

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

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves, I, J. Reine Angew. Math., 212 (1963), 7-25.

Prog

(Magma) for k in[1..200] do if Rank(EllipticCurve([0, 0, 0, k, 0])) eq 0 then print k; end if; end for; // Vaclav Kotesovec, Jul 07 2019
(PARI) for(k=1, 200, if(ellanalyticrank(ellinit([0, 0, 0, k, 0]))[1]==0, print1(k", "))) \\ Seiichi Manyama, Jul 07 2019

Crossrefs

Cf. A002159 (rank 1), A076329 (rank 2).

Cf. A060953.

Sequence in context: A050095 A102528 A325539 * A319829 A272631 A347694

Adjacent sequences: A002155 A002156 A002157 * A002159 A002160 A002161

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Corrected and extended by Vaclav Kotesovec, Jul 07 2019

New name by Vaclav Kotesovec, Jul 07 2019

Status

approved