簡易檢索 / 詳目顯示

研究生: 李忠穎
論文名稱: Computations on the Deuring Correspondence of Supersingular Elliptic Curves
Computations on the Deuring Correspondence of Supersingular Elliptic Curves
指導教授: 紀文鎮
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2007
畢業學年度: 95
語文別: 英文
論文頁數: 25
中文關鍵詞: 橢圓曲線
英文關鍵詞: elliptic curve, supersingular, Deuring, Pizer
論文種類: 學術論文
相關次數: 點閱:156下載:1
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 此篇論文是以實際例子 p=41 之情形, 驗證 Deuring Theorem 的對應性.

    1. Introduction P.1 2. Preliminaries P.1 3. Isogeny Construction P.6 3.1 Case 1, n=2 P.6 3.2 Case 2, n>=3 P.8 3.3 Explicit Generators of End(E) P.10 4. Matching Endomorphism Rings and Maximal Orders P.14 4.1 Backgroung Results of Deuring, Pizer P.14 4.2 Conclusion Based On Our Computations P.18 References P.19 Appendix P.21

    [D1] M. Deuring, Die Anzahl der von Maximalordnungen einer
    definiten Quaternionenalgebra mit primer Grundzahl, Jber.
    Deutch. Math. Verein. 54(1950),24-41.

    [D2] M. Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkorper, Abh. Math. Sem. Hamburg 14(1941), 197-272.

    [M-L] K. MacMurdy and K. Lauter, Explicit Generators for Endomorphism Rings of Supersingular Elliptic Cruves, Preprint, August 2, 2004

    [P1] A. Pizer, The action of the canonical involution ~on
    modular forms of weight 2 on \Gamma _0 (M), Math. Ann. 226(1977),99-116.

    [P2] A. Pizer, A note on a conjecture of Hecke, Pacific J.
    Math. 79(1978), no.2, 541-548.

    [P3] A. Pizer, An algorithm for computing modular forms on \Gamma_0 (N), J. Algebra 64(1980), no.2, 340-390.

    [Sil] J. Silverman, The Arithmetic of Elliptic Curves,
    Graduate Texts in Mathematics 106, Springer-Verlag New York, 1986.

    下載圖示
    QR CODE