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arXiv · 0802.0979

Computing Hilbert Class Polynomials

Juliana Belding·Reinier Bröker·Andreas Enge·Kristin Lauter
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Abstract

We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$, and we show that all methods have comparable run times.

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Juliana Belding, Reinier Bröker, Andreas Enge, Kristin Lauter. 2008-02-07. Computing Hilbert Class Polynomials. https://arxiv.org/abs/0802.0979

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