具N階點之橢圓曲線的參數表示

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。

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.