Abstract
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.
Original language | English |
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Pages (from-to) | 335-343 |
Number of pages | 9 |
Journal | Mathematical Research Letters |
Volume | 19 |
Issue number | 2 |
Publication status | Published - 2012 |