A309032 Numbers k for which rank of the elliptic curve y^2=x^3-k*x is 2.

17, 56, 65, 77, 90, 97, 117, 132, 136, 141, 145, 155, 156, 161, 184, 205, 207, 219, 220, 221, 241, 252, 257, 259, 260, 264, 272, 275, 285, 291, 292, 301, 305, 306, 337, 342, 355, 356, 371, 376, 395, 396, 401, 420, 429, 433, 445, 449, 452, 456, 465, 481, 497, 507, 516

Offset: 1

Author

Seiichi Manyama, Jul 08 2019

Keywords

• nonn

Crossrefs

Cf. A002156 (rank 0), A002157 (rank 1). this sequence (rank 2), A309033 (rank 3), A309034(rank 4).

Cf. A076329.

Programs

Magma

for k in[1..1000] do if Rank(EllipticCurve([0,0,0,-k,0])) eq 2 then print k; end if; end for; // Vaclav Kotesovec, Jul 08 2019

PARI

for(k=1, 1e3, if(ellanalyticrank(ellinit([0, 0, 0, -k, 0]))[1]==2, print1(k", ")))