

A060951


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


9



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
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OFFSET

1,11


COMMENTS

The curves for n and 27*n are isogenous (as Noam Elkies points outsee Womack), so they have the same rank.  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, Minimalknown positive and negative k for Mordell curves of given rank


FORMULA

a(n) = A060950(27*n) and A060950(n) = a(27*n), so a(n) = a(729*n).  Jonathan Sondow, Sep 10 2013


EXAMPLE

a(1) = A060950(27) = a(729) = 0.  Jonathan Sondow, Sep 10 2013


PROG

(PARI) {a(n) = if( n<1, 0, length( ellgenerators( ellinit( [ 0, 0, 0, 0, n], 1))))} /* Michael Somos, Mar 17 2011 */


CROSSREFS

Cf. A060748, A060838, A060950 A060953.
Cf. A081120 (number of integral solutions to Mordell's equation y^2 = x^3  n)
Sequence in context: A230001 A070100 A070095 * A115525 A241910 A065717
Adjacent sequences: A060948 A060949 A060950 * A060952 A060953 A060954


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane, May 10 2001


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.


STATUS

approved



