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A058939
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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 ].
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0, 1, 140, -1372000, -268912000000, 1844736320000000000, 354336952345600000000000000, -2041831254196285440000000000000000000, -366048617485621006827520000000000000000000000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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
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LINKS
| Source
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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
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CROSSREFS
| Sequence in context: A189552 A181238 A185402 * A165600 A137506 A036192
Adjacent sequences: A058936 A058937 A058938 * A058940 A058941 A058942
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KEYWORD
| easy,sign,changed
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AUTHOR
| Graham Everest (g.everest(AT)uea.ac.uk), Jan 12 2001
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