On an explicit upper bound for the degree of an isogeny between two elliptic curves (Q2773289)

The paper gives an explicit bound for the minimal degree of an isogeny between two elliptic curves over a number field, provided one knows that one such isogeny exists. The bound is in terms of the heights of the coefficients of a Weierstrass-equation for one of the curves. The result as well as the methods used in the proof generalise previous work of Masser-Wüstholz and David on the same subject. The author obtains a better numerical constant and better exponents than his predecessors by improving the analytic component of Baker's technique, using multihomogeneous instead of homogeneous auxiliary polynomials.