How would one show that the number of points on the elliptic curve y^2=x^3+B, defined over F_p is p+1, when p is congruent to 2 mod 3?

Thank you

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- Nov 29th 2009, 12:59 PMzverik136elliptic curves over finite fields
How would one show that the number of points on the elliptic curve y^2=x^3+B, defined over F_p is p+1, when p is congruent to 2 mod 3?

Thank you - Nov 30th 2009, 04:44 AMtonio
- Nov 30th 2009, 08:21 AMzverik136
thank you! i did mean over projective space, sorry.

how about for p= 3 mod 4, with Y^2=X^2(X+A), defined over F_p. what bijection could be found? the hint that cassels gives is "consider +/-X together".