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.
https://hal.inria.fr/inria-00246115 Contributor : Andreas EngeConnect in order to contact the contributor Submitted on : Thursday, February 7, 2008 - 2:50:25 PM Last modification on : Friday, February 4, 2022 - 3:14:14 AM Long-term archiving on: : Monday, May 10, 2010 - 12:44:38 PM
Juliana Belding, Reinier Bröker, Andreas Enge, Kristin Lauter. Computing Hilbert Class Polynomials. ANTS-VIII - Eighth Algorithmic Number Theory Symposium, May 2008, Banff, Canada. pp.282-295. ⟨inria-00246115⟩