Sorry not to have got back to you sooner. Hopefully our paper will be up on arXiv soon, but so far I can give you the bounds. Conditionally (on the GRH) they're as follows: Suppose K is a field not containing the Hilbert class field of an imaginary quadratic field. Set S_K the set of primes $\ell$ such that there exists an $\ell$-isogeny. Then the product of all primes in S_K is bounded by something on the order of $\exp((12n)^n(R+h^2\log^2 \Delta)+n^2 h^2 \log^2\Delta)$ where $n$, $\Delta$, $h$, $R$ are the degree, discriminant, class number and regulator of $K$.

Correction to the previous comment: yes, I mean precisely the Mahler measure M (not the Weil height H and not its exp - the paper I looked up had renormalized valuations.)

Yes, I mean basically what Dror said, namely $min_U max_{u_i\in U}H(u_i)$ (or exp of that), where $U$ ranges over fundamental bases and $H=M^{1/n}$ is the Weil height (with $n=deg(K)$). A bound close to $e^R$ would be nice -- the bound I know is on the order of $e^{n^n R}$.