A quasi-linear time algorithm for computing modular polynomials in dimension 2

International audienceWe propose to generalize the work of Régis Dupont for computing modular polynomials in dimension 2 to new invariants. We describe an algorithm to compute modular polynomials for invariants derived from theta constants and prove under some heuristics that this algorithm is quasi-linearin its output size. Some properties of the modular polynomials defined from quotients of theta constants are analyzed.We report on experiments with our implementation