Quantitative upper bounds related to an isogeny criterion for elliptic curves

Let $E_1$ and $E_2$ be two non-CM elliptic curves defined over a number field $K$. By an isogeny theorem due to Kulkarni, Patankar, and Rajan, the two curves are geometrically isogenous if and only if the density of primes for which their Frobenius field coincide is positive. In this talk, we present a quantitative upper bounds of this criterion that improves the result of Baier–Patankar and Wong. The strategy relies on effective versions of the Chebotarev Density Theorem. This is joint work with Alina Cojocaru and Auden Hinz.