Abstract We present an algorithm to compute a higher dimensional analogue of modular polynomials. This higher dimensional analogue, the ‘set of Hilbert modular polynomials’, concerns cyclic isogenies of principally polarised abelian varieties with maximal real multiplication by a fixed totally real number field K 0 . In the 2-dimensional case with K 0 = Q ( 5 ) we also provide an implementation together with some optimisations specific to this case. We also explain applications of this algorithm to point counting, walking on isogeny graphs, and computing class polynomials.

中文翻译：

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希尔伯特模多项式

摘要 我们提出了一种算法来计算模多项式的高维模拟。这种更高维的类似物，即“希尔伯特模多项式集”，涉及主要极化阿贝尔变体的循环同构性，其最大实数乘以固定的全实数域 K 0 。在 K 0 = Q ( 5 ) 的二维情况下，我们还提供了一个实现以及针对这种情况的一些优化。我们还解释了该算法在点计数、等元图上行走和计算类多项式的应用。