92 citations · 1.1k across the 51 of their papers we have counts for
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math.NT2010★ 32 cited
Accelerating the CM method
Andrew V. Sutherland
Given a prime q and a negative discriminant D, the CM method constructs an elliptic curve E/\Fq by obtaining a root of the Hilbert class polynomial H_D(X) modulo q. We consider an…
math.NT2010★ 36 cited
Class invariants by the CRT method
Andreas Enge, Andrew V. Sutherland
We adapt the CRT approach for computing Hilbert class polynomials to handle a wide range of class invariants. For suitable discriminants D, this improves its performance by a large…
math.NT2010★ 57 cited
Modular polynomials via isogeny volcanoes
Reinier Broker, Kristin Lauter, Andrew V. Sutherland
We present a new algorithm to compute the classical modular polynomial Phi_n in the rings Z[X,Y] and (Z/mZ)[X,Y], for a prime n and any positive integer m. Our approach uses the gr…