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

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

Author

N. J. A. Sloane

Keywords

• nonn

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).

Crossrefs

Cf. A060952.

Programs

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

Extensions

Corrected and extended by Vaclav Kotesovec, Jul 07 2019

New name by Vaclav Kotesovec, Jul 07 2019