A002152 Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 1.

2, 4, 7, 13, 15, 18, 19, 20, 21, 22, 23, 25, 28, 29, 30, 35, 38, 40, 43, 44, 45, 48, 49, 50, 51, 54, 55, 56, 57, 58, 59, 60, 63, 65, 66, 71, 72, 74, 75, 79, 81, 84, 85, 87, 91, 93, 94, 95, 100, 101, 102, 107, 110, 112, 115, 120, 123, 124, 126, 127, 128, 129, 130, 131, 135, 137

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.

Programs

Magma

for k in[1..200] do if Rank(EllipticCurve([0,0,0,0,-k])) 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, 0, -k]))[1]==1, print1(k", "))) \\ Seiichi Manyama, Jul 06 2019

Extensions

Better definition from Artur Jasinski, Jun 30 2010

More terms added by Seiichi Manyama, Jul 06 2019