论文标题
CM椭圆曲线附着GALOIS表示的图像有多大？
How big is the image of the Galois representations attached to CM elliptic curves?
论文作者
论文摘要
使用Serre的开放映像定理的类似物，用于具有复杂乘法的椭圆形曲线，可以与每个CM椭圆曲线$ e $相关联，该曲线$ e $ e $定义在数字字段$ f $ a自然数$ \ MATHCAL {i/f）$中，以描述与$ e $相关的galois表示形象多大的图像。我们展示了如何使用我们从复杂乘法的经典理论中获得的封闭公式来计算$ \ Mathcal {i}（e/f）$。
Using an analogue of Serre's open image theorem for elliptic curves with complex multiplication, one can associate to each CM elliptic curve $E$ defined over a number field $F$ a natural number $\mathcal{I}(E/F)$ which describes how big the image of the Galois representation associated to $E$ is. We show how one can compute $\mathcal{I}(E/F)$, using a closed formula that we obtain from the classical theory of complex multiplication.
