

A002159


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


9



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
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OFFSET

1,1


COMMENTS

Terms 80 and 128 are missing in the article by Birch and SwinnertonDyer, 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. SwinnertonDyer, Notes on elliptic curves, I, J. Reine Angew. Math., 212 (1963), 725.


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



