A060965 For p=prime(n), a(n) = number of points (x,y) on the elliptic curve x^3 + y^3 = 1 (mod p), including the point at infinity.

3, 4, 6, 7, 12, 7, 18, 25, 24, 30, 34, 25, 42, 34, 48, 54, 60, 61, 61, 72, 79, 61, 84, 90, 115, 102, 115, 108, 106, 114, 106, 132, 138, 115, 150, 169, 142, 187, 168, 174, 180, 187, 192, 169, 198, 187, 223, 250, 228, 250, 234, 240, 223, 252, 258, 264, 270, 241, 250

Offset

0,1

Comments

Note that the number of points is p+1 when p+1=0 (mod 3); p is a prime in A003627.

Links

Table of n, a(n) for n=0..58.

Example

a(2) = 4 because over GF(3) the points on the curve are (0,1), (1,0), (2,2) and the point at infinity.

Mathematica

Table[p=Prime[n]; s2=Mod[Table[y^3, {y, 0, p-1}], p]; s3=Mod[Table[1-x^3, {x, 0, p-1}], p]; s=Intersection[Union[s2], Union[s3]]; 1+Sum[Count[s2, s[[i]]]*Count[s3, s[[i]]], {i, Length[s]}], {n, 100}] (T. D. Noe)

Crossrefs

Cf. A098514 (number of points on the elliptic curve y^2 = x^3 + x + 1 (mod prime(n))).

Sequence in context: A108797 A089161 A350475 * A153883 A033162 A105133

Adjacent sequences: A060962 A060963 A060964 * A060966 A060967 A060968

Keyword

nonn

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), May 09 2001

Extensions

Edited and extended by T. D. Noe, Sep 14 2004

Status

approved