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Numbers k for which rank of the elliptic curve y^2=x^3-k*x is 3.
5

%I #10 Sep 08 2022 08:46:21

%S 82,226,322,377,442,582,626,706,745,777,799,870,901,910,1042,1045,

%T 1122,1154,1221,1271,1292,1312,1351,1442,1462,1522,1525,1590,1596,

%U 1631,1705,1780,1785,1850,1906,1967,2006,2041,2105,2162,2316,2331,2385,2402,2410,2482,2501,2691

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

%o (PARI) for(k=1, 3e3, if(ellanalyticrank(ellinit([0, 0, 0, -k, 0]))[1]==3, print1(k", ")))

%o (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

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

%Y Cf. A309030.

%K nonn

%O 1,1

%A _Seiichi Manyama_, Jul 08 2019