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math.NT2010
Evaluating Igusa functions
Reinier Broker, Kristin Lauter
The moduli space of principally polarized abelian surfaces is parametrized by three Igusa functions. In this article we investigate a new way to evaluate these functions by using S…
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…