具有有理2-同源约束下最大2-adic像的椭圆曲线模型
Models of Elliptic Curves with Maximal 2-adic Image Subject to a Rational 2-Isogeny
首次发表
浏览论文内容
中文总结 AI 辅助
本文给出在有理2-同源约束下具有最大2-adic像的非CM椭圆曲线的显式模型，利用模曲线与同源图分类使通用性显式化。
中文摘要 AI 辅助
设$E$为定义在$\mathbb{Q}$上的非CM椭圆曲线。我们在曲线具有有理2-同源的约束下，给出了具有尽可能大的2-adic像的曲线模型。已知这些曲线是通用的，本文的目的之一就是使这一事实显式化。我们的技术利用了模曲线及其$j$-映射，以及近期文献中出现的关于同源图分类的结果。
英文摘要
Let $E$ be a non-CM elliptic curve defined over $\mathbb{Q}$. We present models of curves that have 2-adic image as large as possible, given the constraint that they have a rational 2-isogeny. These curves are known to be generic, and one of the aims of this article is to make that fact explicit. Our techniques make use of modular curves and their $j$-maps, as well as classification results on isogeny-graphs that have appeared in the literature recently.
