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%I #12 Nov 23 2022 08:59:28
%S 0,1,140,-1372000,-268912000000,1844736320000000000,
%T 354336952345600000000000000,-2041831254196285440000000000000000000,
%U -366048617485621006827520000000000000000000000000
%N The elliptic divisibility sequence associated to the rational point of smallest known global height for rational elliptic curves: the curve is [ 0,0,0,-412,3316 ] and the point is [ -18,70 ].
%C The terms of the sequence are highly divisible by the primes 2,5 and 7. This is because it is trying to tell us the local heights at the primes where the point [ -18,70 ] has singular reduction on the elliptic curve [ 0,0,0,-412,3316 ].
%C The elliptic curve "280b1" is y^2 = x^3 - 412 * x + 3316. - _Michael Somos_, Feb 12 2012
%H Graham Everest, <a href="https://web.archive.org/web/20070618202920/http://www.mth.uea.ac.uk/~h090/elp.html">Elliptic Divisibility Sequences and the Elliptic Lehmer Problem</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F a(2n+1) = a(n+2)*a(n)^3-a(n-1)*a(n+1)^3, a(2*n) = a(n)*(a(n+2)*a(n-1)^2-a(n-2)*a(n+1)^2)/a(2).
%F a(-n) = -a(n). a(n+2)*a(n-2) = 19600 * a(n+1)*a(n-1) + 1372000 * a(n)^2. a(n+3)*a(n-2) = -1372000 * a(n+2)*a(n-1) + 1920800000 * a(n+1)*a(n). - _Michael Somos_, Feb 12 2012
%K easy,sign
%O 0,3
%A Graham Everest (g.everest(AT)uea.ac.uk), Jan 12 2001
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