A002157 Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 1.

2, 5, 6, 7, 10, 12, 14, 15, 20, 21, 22, 23, 25, 26, 30, 31, 32, 34, 36, 37, 38, 39, 41, 42, 45, 46, 47, 49, 50, 52, 53, 54, 55, 57, 58, 60, 62, 66, 69, 70, 71, 72, 73, 74, 76, 78, 79, 80, 84, 85, 86, 87, 89, 94, 95, 96, 99, 101, 102, 103, 105, 106, 110, 111, 112, 114, 116

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

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

Crossrefs

Cf. A060952.

Programs

Magma

for k in[1..200] do if Rank(EllipticCurve([0,0,0,-k,0])) eq 1 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]==1, print1(k", "))) \\ Seiichi Manyama, Jul 07 2019

Extensions

More terms added by Seiichi Manyama, Jul 07 2019