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%I #7 Mar 30 2012 17:22:33
%S 2,3,8,4,13,17,17,20,27,35,32,47,34,33,59,57,62,49,55,58,71,85,89,99,
%T 96,104,86,104,122,124,125,127,125,125,135,153,170,188,143,171,179,
%U 189,216,200,221,217,222,243,227,231,236,261,219,281,248,259,293,273,255,288
%N For p=prime(n), a(n) = number of points (x,y) on the elliptic curve y^2 = x^3 + x + 1 (mod p), not including the point at infinity.
%C This is one of the simplest non-degenerate elliptic curves. A theorem of Hasse states that the number of points (including the point at infinity) is p+1+d, where |d| < 2 sqrt(p).
%H T. D. Noe, <a href="/A098514/b098514.txt">Table of n, a(n) for n=1..1000</a>
%H Joseph H. Silverman, <a href="http://www.math.brown.edu/~jhs/UbiquityOfEllipticCurves.ppt">The Ubiquity of Elliptic Curves (PowerPoint)</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EllipticCurve.html">Elliptic Curve</a>
%t Table[p=Prime[n]; s2=Mod[Table[y^2, {y, 0, p-1}], p]; s3=Mod[Table[x^3+x+1, {x, 0, p-1}], p]; s=Intersection[Union[s2], Union[s3]]; Sum[Count[s2, s[[i]]]*Count[s3, s[[i]]], {i, Length[s]}], {n, 100}]
%Y Cf. A098513 (number of points on the elliptic curve y^2 = x^3 + x + 1 (mod n)).
%K nonn
%O 1,1
%A _T. D. Noe_, Sep 11 2004
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