Module Structures of the Elliptic Curves over finite Field of Characteristic ≠ 2,3
碩士 === 國立清華大學 === 數學系 === 92 === Let E/K be an elliptic curve defined over an imaginary quadratic field $K$ with complex multiplication by the ring of integers $R_K$ of $K$. For $\idealP$, prime of $K$ at which $E$ has good reduction, let $k_{\idealP}:=R_K/\idealP$ and $\tilde{E}/k_{\idealP}$ be the...
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| Format: | Others |
| Language: | en_US |
| Published: |
2004
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| Online Access: | http://ndltd.ncl.edu.tw/handle/71342853949633331708 |
| Summary: | 碩士 === 國立清華大學 === 數學系 === 92 === Let E/K be an elliptic curve defined over an imaginary quadratic field $K$ with complex multiplication by the ring of integers $R_K$ of $K$. For $\idealP$, prime of $K$ at which $E$ has good reduction, let $k_{\idealP}:=R_K/\idealP$ and $\tilde{E}/k_{\idealP}$ be the reduction of $E$ modulo $\idealP$.
Our main purpose is to study the $R_K$-Module structure of
$\tilde{E}(k_{\idealP})$ as $E$ to be the following two families of elliptic curves, $E_D:y^2=x^3-Dx$, $E^D:y^2=x^3+D$, for all $D\in\ZZ$.
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