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A002157
Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 1.
(Formerly M1317 N0505)
5
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
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
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
KEYWORD
nonn
EXTENSIONS
More terms added by Seiichi Manyama, Jul 07 2019
STATUS
approved