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URL: https://oeis.org/A002158

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A002158
Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 0.
6
1, 2, 4, 6, 7, 10, 11, 12, 16, 17, 22, 23, 25, 26, 27, 30, 32, 36, 38, 41, 42, 43, 44, 45, 50, 52, 54, 57, 58, 59, 62, 64, 70, 71, 72, 74, 75, 76, 78, 81, 82, 86, 87, 91, 96, 97, 102, 103, 106, 107, 108, 110, 112, 116, 117, 118, 119, 122, 123, 130, 132, 134, 135, 137, 139, 140, 142, 146, 147, 151, 160, 161, 162, 166, 167, 169, 170, 172, 174, 176, 177, 182, 186, 187, 190, 192, 193, 194, 199
OFFSET
1,2
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
(Magma) for k in[1..200] do if Rank(EllipticCurve([0, 0, 0, k, 0])) eq 0 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]==0, print1(k", "))) \\ Seiichi Manyama, Jul 07 2019
CROSSREFS
Cf. A002159 (rank 1), A076329 (rank 2).
Cf. A060953.
Sequence in context: A050095 A102528 A325539 * A319829 A272631 A347694
KEYWORD
nonn
EXTENSIONS
Corrected and extended by Vaclav Kotesovec, Jul 07 2019
New name by Vaclav Kotesovec, Jul 07 2019
STATUS
approved