Contents Online
Mathematical Research Letters
Volume 19 (2012)
Number 2
Isomorphism classes of elliptic curves over a finite field in some thin families
Pages: 335 – 343
DOI: https://dx.doi.org/10.4310/MRL.2012.v19.n2.a6
Authors
Abstract
For a prime $p$ and a given square box, $\B$, we consider allelliptic curves $E_{r,s}:Y^2=X^3+rX+s$ defined over a field$\F_p$ of $p$ elements with coefficients $(r,s)\in\B$. Weobtain a nontrivial upper bound for the number of suchcurves which are isomorphic to a given one over $\F_p$, interms of the size of $\B$. We also give an optimal lowerbound on the number of distinct isomorphic classesrepresented.
Published 12 July 2012