Foraprime p and a given square box, B, we consider all elliptic curves E r,s: Y 2 = X 3 +rX +s defined over a field F pp of p elements with coefficients (r, s) ∈ B. We obtain a nontrivial upper bound for the number of such curves which are isomorphic to a given one over F p, in terms of the size of B. We also give an optimal lower bound on the number of distinct isomorphic classes represented.
|Number of pages||9|
|Journal||Mathematical Research Letters|
|Publication status||Published - 2012|