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, 1, 140, -1372000, -268912000000, 1844736320000000000, 354336952345600000000000000, -2041831254196285440000000000000000000, -366048617485621006827520000000000000000000000000

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

Table of n, a(n) for n=0..8.

Graham Everest, Elliptic Divisibility Sequences and the Elliptic Lehmer Problem

Index to divisibility sequences

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

Adjacent sequences: A058936 A058937 A058938 * A058940 A058941 A058942

Keyword

easy,sign

Author

Graham Everest (g.everest(AT)uea.ac.uk), Jan 12 2001

Status

approved