A060953 Rank of elliptic curve y^2 = x^3 + n*x.

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

Offset: 1

Author

N. J. A. Sloane, May 10 2001

Keywords

• nonn
• nice

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• H. Mishima, Tables of Elliptic Curves
• F. Richman, Elliptic curves
• K. Rubin and A. Silverberg, Ranks of elliptic curves

Crossrefs

Cf. A060748, A060838, A060950-A060953.

Programs

PARI

{ A060953(n) = ellanalyticrank( ellinit([0,0,0,n,0]) )[1]; }

Formula

a(-n) = A060952(n). - Michael Somos, Dec 15 2011

Extensions

Lambert Klasen (Lambert.Klasen(AT)gmx.net), Mar 31 2005, kindly rechecked this sequence against the Mishima web site and found no errors.

Corrected Apr 10 2005 at the suggestion of James R. Buddenhagen. There were errors caused by the fact that Mishima lists each curve of rank two twice, once for each generator.

Extended by Max Alekseyev, Mar 09 2009