In this paper, we present a description of the [Formula: see text]-adic Galois representation attached to an elliptic curve defined over a [Formula: see text]-adic field [Formula: see text], in the case where the image of inertia is non-abelian. There are two possibilities for the image of inertia, namely [Formula: see text] and [Formula: see text], and in each case, we need to distinguish whether the inertia degree of [Formula: see text] over [Formula: see text] is even or odd. The results presented here are being implemented in an algorithm to compute explicitly the Galois representation in these four cases.

中文翻译：

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Wild Galois 表示：具有非阿贝尔惯性作用的 2 进场上的椭圆曲线

在本文中，我们描述了 [Formula: see text]-adic Galois 表示附加到在 [Formula: see text]-adic 字段 [Formula: see text] 上定义的椭圆曲线，在图像的情况下惯性是非阿贝尔的。惯性形象有两种可能，分别是【公式：见文】和【公式：见文】，在每种情况下，我们都需要区分【公式：见文】的惯性程度是否高于【公式：见text] 是偶数或奇数。这里给出的结果正在一个算法中实现，以明确计算这四种情况下的伽罗瓦表示。