OFFSET
1,1
COMMENTS
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).
LINKS
T. D. Noe, Table of n, a(n) for n=1..1000
Joseph H. Silverman, The Ubiquity of Elliptic Curves (PowerPoint)
Eric Weisstein's World of Mathematics, Elliptic Curve
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Sep 11 2004
STATUS
approved