Isomorphism classes of elliptic curves over a finite field in some thin families

Javier Cilleruelo*, Igor E. Shparlinski, Ana Zumalacárregui

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

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 languageEnglish
Pages (from-to)335-343
Number of pages9
JournalMathematical Research Letters
Volume19
Issue number2
Publication statusPublished - 2012

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