A319510 Rank of elliptic curve y^2 = x^3 - n^2 * x.

0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0

Offset: 1

Author

Seiichi Manyama, Sep 24 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A003273, A060952, A062693, A062695, A194687, A273929.

Programs

PARI

{a(n) = ellanalyticrank(ellinit([0, 0, 0, -n^2, 0]))[1]}

Formula

a(n) = A060952(n^2).

a(A003273(n)) > 0.

a(A194687(n)) = n.

Empirical: a(n) = a(4*n). - Jose Aranda, Jul 02 2024