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Old 2021-01-28, 11:34   #1
RedGolpe
 
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Aug 2006
Monza, Italy

73 Posts
Default Number of points on elliptic curves over finite fields

Hi all, I noticed that for elliptic curves of the form

y2x3 + 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 2021-01-28 at 11:46 Reason: more info
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