Yingkun Li (Wisconsin)

Isogenies between CM elliptic curves

Given two CM elliptic curves over a number field K, it is well-known that there is a positive density of rational primes p such that there exist a prime $\mathfrak{p}$ in K above p, modulo which the two curves are isogenous. If one fixes the degree of the isogeny to be m, then there could be only finitely many such rational primes p, bounded by $m^2$. In this talk, we will look at some lower bounds of the number of such primes, based on a joint work with Edgar Assing, Jiacheng Xia and Tian Wang.