发表机构
Universidad de Sevilla（塞维利亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对在二次域上挠群增长的有理椭圆曲线，结合曲线不变量，计算添加素数阶挠点时二次域的分歧情况，拓展了此前关于椭圆曲线导子素数与二次域判别式素数关联的研究。
AI 中文摘要
设$E/\boldsymbol{\text{Q}}$为在二次域$K$上挠群发生增长的有理椭圆曲线。在之前的论文中，已证明$E$的导子素数与整除$K$判别式的素数之间存在关联。本文在该研究基础上进一步推进，结合曲线的不变量，计算当添加素数阶$\boldsymbol{\text{ℓ}}$的挠点时，域$K$的分歧情况，具体涉及导子、素数$\boldsymbol{\text{ℓ}}$以及坏约化素数处的Kodaira符号。
英文摘要
Let $E/\mathbb{Q}$ be a rational elliptic curve whose torsion group grows over a quadratic field $K$. In a previous paper, a relation between the primes of the conductor of $E$ and the primes that divide the discriminant of $K$ was shown. In the present paper, we go further in this study and we compute the ramification of the field $K$, when a torsion point of prime order $\ell$ is added, in terms of invariants of the curve. Concretely, the conductor, the prime $\ell$ and the Kodaira symbol at the primes of bad reduction.
