Nicolas Billerey (Essen)
Isogenies of prime degree over number fields
Abstract:
Let E be an elliptic curve defined over a number field K. The
so-called exceptional set for (E,K) consisting of prime numbers p such
that E has a p-isogeny defined over K is finite iff E does not have CM
over K. In this talk, I will state a criterion which allows (at least
when K is quadratic or has odd degree) to explicitly determine the
exceptional set when it is finite.