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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 楊一帆 | zh_TW |
| dc.contributor.advisor | Yi-Fan Yang | en |
| dc.contributor.author | 林侑勳 | zh_TW |
| dc.contributor.author | Yuw-Hsun Lin | en |
| dc.date.accessioned | 2025-07-23T16:15:45Z | - |
| dc.date.available | 2025-07-24 | - |
| dc.date.copyright | 2025-07-23 | - |
| dc.date.issued | 2025 | - |
| dc.date.submitted | 2025-07-17 | - |
| dc.identifier.citation | [1] H. Baaziz. Equations for the modular curve X1(N) and models of elliptic curves with torsion points. MATHEMATICS OF COMPUTATION, 79(272): 2371–2386, 2010.
[2] H. Cohen and F. Strömberg. Modular Form: A Classical Approach, volume 179 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2017. [3] P. Deligne and M. Rapoport. Les schémas de modules de courbes elliptiques. In P. Deligne and W. Kuijk, editors, Modular Functions of One Variable II, pages 143–316, Berlin, Heidelberg, 1973. Springer Berlin Heidelberg. ISBN 978-3-540-37855-6. [4] J. S. Fred Diamond. A First Course in Modular Forms. Springer New York, NY, 2010. [5] T. Miyake. Modular Forms. Springer Berlin, Heidelberg, 2005. [6] J. H. Silverman. The Arithmetic of Elliptic Curves. Springer New York, NY, 2nd edition, 2009. [7] Y. Yang. Transformation formulas for generalized dedekind eta functions. Bulletin of the London Mathematical Society, 36(5):671–682, 2004. [8] Y. Yang. Defining equations of modular curves. Advances in Mathematics,204(2):481–508, 2006. ISSN 0001-8708. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/97962 | - |
| dc.description.abstract | 本論文探討帶有N階點的橢圓曲線組成之模空間，其中N為4到20之間的整數。目標是將橢圓曲線之Tate標準形式的係數，以明確的模函數表示。這些模函數由廣義戴德金η函數組成，並且生成由對應模群Γ1(N)的模函數組成的體。 | zh_TW |
| dc.description.abstract | In this thesis, we study the moduli space of elliptic curves with a specified N-torsion, for 4 ≤ N ≤ 20. Our focus is on expressing the coefficients of the Tate normal form of elliptic curves in terms of explicit modular functions. These modular functions are specific generators for the field of modular functions on Γ1(N) constructed from Generalized η-functions. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2025-07-23T16:15:45Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2025-07-23T16:15:45Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix List of Tables xi Chapter 1 Introduction 1 Chapter 2 Preliminaries 3 2.1 Complex Elliptic Curves 3 2.2 Tate Normal Form 9 2.3 Modular Forms and Modular Functions 12 2.4 Valence Formula 19 2.5 Transformation Formula for ℘(sτ + t; τ ) 20 2.6 Elliptic Function and Jacobi Theta Functions 23 2.7 Generalized Dedekind Eta Function 25 2.8 Generators for the field of modular functions with respect to Γ1(N) 27 Chapter 3 Main Result 31 3.1 The order at cusps of f and g 31 3.2 A representation of f and g in terms of generators 38 3.3 Table of Results 43 References 47 | - |
| dc.language.iso | en | - |
| dc.subject | 模形式 | zh_TW |
| dc.subject | 模形式 | zh_TW |
| dc.subject | Tate Normal Form | en |
| dc.subject | Modular Form | en |
| dc.subject | Tate Normal Form | en |
| dc.subject | Modular Form | en |
| dc.title | 具N階點之橢圓曲線的參數表示 | zh_TW |
| dc.title | Explicit parametrizations of elliptic curves with N-torsions | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 113-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 李庭諭;凃芳婷 | zh_TW |
| dc.contributor.oralexamcommittee | Ting-Yu Lee;Fang-Ting Tu | en |
| dc.subject.keyword | 模形式, | zh_TW |
| dc.subject.keyword | Modular Form,Tate Normal Form, | en |
| dc.relation.page | 48 | - |
| dc.identifier.doi | 10.6342/NTU202501859 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2025-07-18 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| dc.date.embargo-lift | 2025-07-24 | - |
| Appears in Collections: | 數學系 | |
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| File | Size | Format | |
|---|---|---|---|
| ntu-113-2.pdf | 692.51 kB | Adobe PDF | View/Open |
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