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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2004
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| Online Access: | http://ndltd.ncl.edu.tw/handle/71342853949633331708 |
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ndltd-TW-092NTHU54790112015-10-13T13:08:04Z http://ndltd.ncl.edu.tw/handle/71342853949633331708 Module Structures of the Elliptic Curves over finite Field of Characteristic ≠ 2,3 特徵值不等於2或3之有限體上橢圓曲線的模結構 Ting-Chao Wang 王廷朝 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 $D\in\ZZ$. Jing Yu 于靖 2004 學位論文 ; thesis 37 en_US |
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en_US |
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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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| author2 |
Jing Yu |
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Jing Yu Ting-Chao Wang 王廷朝 |
| author |
Ting-Chao Wang 王廷朝 |
| spellingShingle |
Ting-Chao Wang 王廷朝 Module Structures of the Elliptic Curves over finite Field of Characteristic ≠ 2,3 |
| author_sort |
Ting-Chao Wang |
| title |
Module Structures of the Elliptic Curves over finite Field of Characteristic ≠ 2,3 |
| title_short |
Module Structures of the Elliptic Curves over finite Field of Characteristic ≠ 2,3 |
| title_full |
Module Structures of the Elliptic Curves over finite Field of Characteristic ≠ 2,3 |
| title_fullStr |
Module Structures of the Elliptic Curves over finite Field of Characteristic ≠ 2,3 |
| title_full_unstemmed |
Module Structures of the Elliptic Curves over finite Field of Characteristic ≠ 2,3 |
| title_sort |
module structures of the elliptic curves over finite field of characteristic ≠ 2,3 |
| publishDate |
2004 |
| url |
http://ndltd.ncl.edu.tw/handle/71342853949633331708 |
| work_keys_str_mv |
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