A002159 - OEIS

A002159

Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 1.
(Formerly M2429 N0962)

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

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

OFFSET

1,1

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.

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. A060953, A076329.

Sequence in context: A325540 A102529 A186621 * A050094 A137319 A138808

Adjacent sequences: A002156 A002157 A002158 * A002160 A002161 A002162

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms added by Seiichi Manyama, Jul 07 2019

STATUS

approved