A309060 Least k such that the rank of the elliptic curve y^2 = x^3 + k^2*x is n.

1, 3, 17, 627, 14637

Offset: 0

Author

Seiichi Manyama, Jul 09 2019

Keywords

• nonn
• more
• hard

Comments

From Jose Aranda, Jun 30 2024: (Start)

A319510(n even) = A309061(n/2), A319510(n odd) = A309061(2*n) (Empirical).

A194687(5) = 48272239 which implies a(5) <= 96544478 (Checked).

A194687(6) = 6611719866 which implies a(6) <= 3305859933 (Checked).

A194687(7) <= 797507543735 which implies a(7) <= 1595015087470 (Checked). (End)

Examples

			A309061(1) = 0.
A309061(3) = 1.
A309061(17) = 2.
		

Crossrefs

Cf. A194687, A309028, A309061, A319510.

Programs

PARI

{a(n) = my(k=1); while(ellanalyticrank(ellinit([0, 0, 0, k^2, 0]))[1]<>n, k++); k}

Formula

A309061(a(n)) = n.