Number of points on elliptic curves over finite fields
Hi all, I noticed that for elliptic curves of the form
y^{2} ≡ x^{3} + a (mod p)
sometimes the number of points is always p+1 for any choice of a. This seems to be the case for all p ≡ 5 (mod 6).
Moreover, when this does not happen, i.e., for p ≡ 1 (mod 6), it looks like there are exactly zero curves of such form where the number of points is p+1.
Can someone point me towards the right direction as to why this happens?
Last fiddled with by RedGolpe on 20210128 at 11:46
Reason: more info
