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Ìý Given an elliptic curve E over Q, a celebrated conjecture of GoldfeldÌýasserts that a positive proportion of its quadratic twists should haveÌýanalytic rank 0 (resp. 1). We show this conjecture holds whenever E has aÌýrational 3-isogeny. We also prove the analogous result for the sexticÌýtwists of j-invariant 0 curves. For a more general elliptic curve E, weÌýshow that the number of quadratic twists of E up to twisting discriminant XÌýof analytic rank 0 (resp. 1) is >> X/log^{5/6}X, improving the current bestÌýgeneral bound towards Goldfeld's conjecture due to Ono-Skinner (resp.ÌýPerelli-Pomykala). We prove these results by establishing a congruenceÌýformula between p-adic logarithms of Heegner points based on Coleman'sÌýintegration. This is joint work with Daniel Kriz.