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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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
Quote:
Originally Posted by zverik136
You mean over projective space, right? Anyway, as, the map
is an automorphism of
, and thus
is a bijection between
the set of points of the elliptic curve in
. Now add the point at infinity in projective space and we're done.
Tonio
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".