A002157 - OEIS

A002157

Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 1.
(Formerly M1317 N0505)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

Table of n, a(n) for n=1..67.

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

PROG

(PARI) for(k=1, 200, if(ellanalyticrank(ellinit([0, 0, 0, -k, 0]))[1]==1, print1(k", "))) \\ Seiichi Manyama, Jul 07 2019

(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

CROSSREFS

Cf. A060952.

Sequence in context: A087791 A334880 A285032 * A050002 A047578 A259605

Adjacent sequences: A002154 A002155 A002156 * A002158 A002159 A002160

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms added by Seiichi Manyama, Jul 07 2019

STATUS

approved