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Author: William A. Stein
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\noindent{\bf Abstract}
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for {\it The field generated by the points of small prime
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order on an elliptic curve}
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We prove that the field generated by the points
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of order~$p$ of an elliptic curve over~$\bar {\bf Q}$ is strictly bigger than
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the cyclotomic field generated by $p$th roots of unity, for~$p$ a prime
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number satisfying $p=11$ or $17\le p<1000$.
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