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A060951
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Rank of elliptic curve y^2 = x^3 - n.
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11
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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
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1,11
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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PROG
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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 */
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CROSSREFS
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Cf. A081120 (number of integral solutions to Mordell's equation y^2 = x^3 - n).
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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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.
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STATUS
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approved
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