同构N-挠椭圆曲线对的模
Moduli for Pairs of Elliptic Curves with Isomorphic N-torsion
摘要：
研究了椭圆曲线对的模曲面及其N-挠群之间的同构。Weil配对给出了从这个模量表面到（Z/NZ）* 的“行列式”映射;它的纤维是表面的组成部分。我们定义空间的模形式在这些组件和Hecke之间的对应关系，并研究这些空间的模形式的行为作为模块的Hecke代数。我们发现行列式为-1的分支在某种程度上是“支配”分支;我们用复乘形式刻画了它的模形式空间与其它分支上的模形式空间的区别。最后，我们展示了当N是素数时出现的一些简化，包括这种CM形式的完整确定，并给出了数值例子。
英文摘要：
We study the moduli surface for pairs of elliptic curves together with an isomorphism between their N-torsion groups. The Weil pairing gives a "determinant" map from this moduli surface to (Z/NZ)*; its fibers are the components of the surface. We define spaces of modular forms on these components and Hecke correspondences between them, and study how those spaces of modular forms behave as modules for the Hecke algebra. We discover that the component with determinant -1 is somehow the "dominant" one; we characterize the difference between its spaces of modular forms and the spaces of modular forms on the other components using forms with complex multiplication. Finally, we show some simplifications that arise when N is prime, including a complete determination of such CM-forms, and give numerical examples.
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