Isomorphism Classes of Elliptic Curves Over a Finite Field in Some Thin Families
نویسندگان
چکیده
We give a non trivial upper bound for the number of elliptic curves Er,s : Y 2 = X3 + rX + s with (r, s) ∈ [R + 1, R + M ]× [S + 1, S + M ] that are isomorphic to a given curve. We also give an almost optimal lower bound for the number of distinct isomorphic classes represented by elliptic curves Er,s with the coefficients r, s lying in a small box.
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