\magnification=1200 \pretolerance=200 \tolerance=400 \brokenpenalty=200 \font\titchap=cmr17 at 17pt % pour les titres de chapitres \noindent{\bf Abstract} for {\it The field generated by the points of small prime order on an elliptic curve} \vskip .3in We prove that the field generated by the points of order~$p$ of an elliptic curve over~$\bar {\bf Q}$ is strictly bigger than the cyclotomic field generated by $p$th roots of unity, for~$p$ a prime number satisfying $p=11$ or $17\le p<1000$. \bye