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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS The curves for n and -27*n are isogenous (as Noam Elkies points out--see 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 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

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Last modified October 21 13:24 EDT 2019. Contains 328299 sequences. (Running on oeis4.)