A309033 Numbers k for which rank of the elliptic curve y^2=x^3-k*x is 3.

82, 226, 322, 377, 442, 582, 626, 706, 745, 777, 799, 870, 901, 910, 1042, 1045, 1122, 1154, 1221, 1271, 1292, 1312, 1351, 1442, 1462, 1522, 1525, 1590, 1596, 1631, 1705, 1780, 1785, 1850, 1906, 1967, 2006, 2041, 2105, 2162, 2316, 2331, 2385, 2402, 2410, 2482, 2501, 2691

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Prog

(PARI) for(k=1, 3e3, if(ellanalyticrank(ellinit([0, 0, 0, -k, 0]))[1]==3, print1(k", ")))
(Magma) for k in[1..3000] do if Rank(EllipticCurve([0, 0, 0, -k, 0])) eq 3 then print k; end if; end for; // Vaclav Kotesovec, Jul 08 2019

Crossrefs

Cf. A002156 (rank 0), A002157 (rank 1). A309032 (rank 2), this sequence (rank 3), A309034 (rank 4).

Cf. A309030.

Sequence in context: A092229 A304548 A316373 * A306133 A317268 A258739

Adjacent sequences: A309030 A309031 A309032 * A309034 A309035 A309036

Keyword

nonn

Author

Seiichi Manyama, Jul 08 2019

Status

approved