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

0,2

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)

Links

Table of n, a(n) for n=0..4.

Formula

A309061(a(n)) = n.

Example

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

Prog

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

Crossrefs

Cf. A194687, A309028, A309061, A319510.

Sequence in context: A094133 A049985 A126579 * A270816 A217957 A252730

Adjacent sequences: A309057 A309058 A309059 * A309061 A309062 A309063

Keyword

nonn,more,hard

Author

Seiichi Manyama, Jul 09 2019

Status

approved