A002156 Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 0. (Formerly M2345 N0926)

1, 3, 4, 8, 9, 11, 13, 16, 18, 19, 24, 27, 28, 29, 33, 35, 40, 43, 44, 48, 51, 59, 61, 63, 64, 67, 68, 75, 81, 83, 88, 91, 92, 93, 98, 100, 104, 107, 108, 109, 113, 115, 120, 121, 123, 125, 126, 128, 129, 131, 139, 144, 152, 153, 157, 163, 164, 168, 172, 173, 176, 177, 179, 180, 187, 189, 193, 195, 198, 200

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..1730

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

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

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. A060952.

Sequence in context: A006520 A054204 A050003 * A285033 A073258 A170954

Adjacent sequences: A002153 A002154 A002155 * A002157 A002158 A002159

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