Computing Hilbert Class Polynomials
  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. 
Juliana Belding, Reinier Br\"oker, Andreas Enge (INRIA Futurs),   Kristin Lauter