A060951 Rank of elliptic curve y^2 = x^3 - n.
0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 2
Offset: 1
Examples
a(1) = A060950(27) = a(729) = 0. - _Jonathan Sondow_, Sep 10 2013
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000 (from Gebel)
- J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
- H. Mishima, Tables of Elliptic Curves
- T. Womack, Minimal-known positive and negative k for Mordell curves of given rank
Crossrefs
Programs
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PARI
{a(n) = if( n<1, 0, length( ellgenerators( ellinit( [ 0, 0, 0, 0, -n], 1))))} /* Michael Somos, Mar 17 2011 */ -
PARI
apply( {A060951(n)=ellrank(ellinit([0,-n]))[1]}, [1..99]) \\ For version < 2.14, use ellanalyticrank(...). - M. F. Hasler, Jul 01 2024
Formula
Extensions
Corrected Apr 08 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.
Comments