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A058939 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 ]. 0
0, 1, 140, -1372000, -268912000000, 1844736320000000000, 354336952345600000000000000, -2041831254196285440000000000000000000, -366048617485621006827520000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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 ].
The elliptic curve "280b1" is y^2 = x^3 - 412 * x + 3316. - Michael Somos, Feb 12 2012
LINKS
FORMULA
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).
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
CROSSREFS
Sequence in context: A185402 A216729 A350614 * A214376 A165600 A137506
KEYWORD
easy,sign
AUTHOR
Graham Everest (g.everest(AT)uea.ac.uk), Jan 12 2001
STATUS
approved

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)