A309034 Numbers k for which rank of the elliptic curve y^2=x^3-k*x is 4.

5037, 5795, 6497, 7585, 7672, 8701, 10001, 10081, 10605, 14547, 14637, 15805, 20091, 20737, 20760, 21177, 21571, 22321, 23137, 24492, 27812, 30877, 31595, 33026, 34241, 36737, 38412, 38497, 41021, 41907, 41922, 42347, 43036

Offset: 1

Author

Seiichi Manyama, Jul 08 2019

Keywords

• nonn

Crossrefs

Cf. A002156 (rank 0), A002157 (rank 1). A309032 (rank 2), A309033 (rank 3), this sequence (rank 4), A309100 (rank 5).

Cf. A060952, A309031.

Programs

Magma

for k in[1..10000] do if Rank(EllipticCurve([0,0,0,-k,0])) eq 4 then print k; end if; end for; // Vaclav Kotesovec, Jul 08 2019

PARI

for(k=1, 1e4, if(ellanalyticrank(ellinit([0, 0, 0, -k, 0]))[1]==4, print1(k", ")))

Extensions

a(29)-a(33) from Seiichi Manyama, Jul 09 2019