The Zilber-Pink conjecture predicts that there should be only finitely
many algebraic numbers t such that the three elliptic curves with
j-invariants t, -t, 2t are all isogenous to each other. Using previous
work of Habegger and Pila, it suffices to prove a height bound for such
t. I will outline the proof of this height bound by viewing periods of
the elliptic curves as values of G-functions. An innovation in this
work is that both complex and p-adic periods are required. This is
joint work with Christopher Daw.
