论文标题
具有指定扭转亚组的良好椭圆曲线
Good elliptic curves with a specified torsion subgroup
论文作者
论文摘要
如果$ n_ {e}^{e}^{6} <\ max \！\！\！\！ $ e $和$ c_ {4} $和$ c_ {6} $的导体是与$ e $的全局最小模型相关的不变性。在本文中，我们概括了Masser的定理，内容是无限的许多优质椭圆曲线，并全额为2美元。具体来说，我们通过建设性方法证明，对于Mazur的Torsion Terorem允许的15个Torsion子组中的每一种，都有无限的许多优质椭圆曲线$ E $带有$ e \！\！\！\！\！
An elliptic curve $E$ over $\mathbb{Q}$ is said to be good if $N_{E}^{6}<\max\!\left\{ \left\vert c_{4}^{3}\right\vert ,c_{6}^{2}\right\} $ where $N_{E}$ is the conductor of $E$ and $c_{4}$ and $c_{6}$ are the invariants associated to a global minimal model of $E$. In this article, we generalize Masser's Theorem on the existence of infinitely many good elliptic curves with full $2$-torsion. Specifically, we prove via constructive methods that for each of the fifteen torsion subgroups $T$ allowed by Mazur's Torsion Theorem, there are infinitely many good elliptic curves $E$ with $E\!\left(\mathbb{Q}\right) _{\text{tors}}\cong T$.
