17 citations · 19 across the 6 of their papers we have counts for
6 papers
Using Fricke modular polynomials to compute isogenies
François Morain
Let be an elliptic curve over a field and a prime. There exists an elliptic curve related to by an isogeny of degree…
Using the Charlap-Coley-Robbins polynomials for computing isogenies
François Morain
The SEA algorithm for computing the cardinality of elliptic curves over finite fields in many characteristic uses modular polynomials. These polynomials come into different flavors…
Computing the Charlap-Coley-Robbins modular polynomials
François Morain
Let be an elliptic curve over a field and a prime. There exists an elliptic curve related to by anisogeny (rational map that…
Modular equations for some -products
François Morain
The classical modular equations involve bivariate polynomials that can be seen to be univariate with coefficients in the modular invariant . Kiepert found modular equations rela…
Generalised Weber Functions
Andreas Enge, François Morain
A generalised Weber function is given by $\w_N(z) = η(z/N)/η(z)$, where is the Dedekind function and is any integer; the original function corresponds to . We class…
Edwards curves and CM curves
François Morain
Edwards curves are a particular form of elliptic curves that admit a fast, unified and complete addition law. Relations between Edwards curves and Montgomery curves have already be…