Approximation to the transcendental relationship of two algebraic points of the function $\wp(z)$ with complex multiplication

For fixed $\varepsilon>0$, the following inequality holds:
$$ \Bigl|\frac uv-\beta\Bigr|>C\exp(-(\ln H)^{2+\varepsilon}) $$
for all numbers $\beta$ belonging to a field $K$ of finite degree over $Q$. The constant $C>0$ does not depend on beta. $H$ is the height of beta. $\wp(u)$ and $\wp(v)$ are algebraic numbers, and $u/v$ is a transcendental number. $\wp(z)$ is the Weierstrass function with complex multiplication and algebraic invariants. The proof is ineffective.