A002159 Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 1.

3, 5, 8, 9, 13, 15, 18, 19, 20, 21, 24, 28, 29, 31, 35, 37, 40, 47, 48, 49, 51, 53, 56, 60, 61, 67, 69, 77, 79, 80, 83, 84, 85, 88, 90, 92, 93, 95, 98, 100, 101, 104, 109, 111, 115, 120, 121, 124, 125, 126, 127, 128, 131, 133, 136, 141, 143, 144, 148, 149, 152, 153, 156

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Terms 80 and 128 are missing in the article by Birch and Swinnerton-Dyer, page 25, table 4b. - Vaclav Kotesovec, Jul 07 2019

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..2040
• B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves, I, J. Reine Angew. Math., 212 (1963), 7-25.

Crossrefs

Cf. A060953, A076329.

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