A Lehmer-Type Lower Bound for the Canonical Height on Elliptic Curves Over Function Fields

Let F be the function field of a curve over an algebraically closed field with char(F)≠2,3, and let E/F be an elliptic curve. Then for all finite separable extensions K/F and all non-torsion points P∈E(K), the F-normalized canonical height of P is bounded below by \[ ĥ_E(P) ≥ {1}{7496· hF(j_E)²· [K:F]²}. \]