In equation 2.10 of this article, the author gives the Seiberg-Witten curve for a $U(N)$ gauge theory with $L<2N$ massive flavours with masses given by $m_i$ as:

$y^{2}=\left\langle \mathrm{det}\left(z\mathbb{I}-\Phi\right)\right\rangle ^{2}-4\Lambda^{2N-L}\prod_{i=1}^{L}\left(z+m_{i}\right)$

Where $\Lambda$ is the cutoff scale of the theory, and $\Phi$ is the adjoint scalar in the vector multiplet.

Does anyone know what the analogous equation for a product $SU(2)^N$ gauge theory is? There is a discussion of such Seiberg-Witten curves in e.g. this article by Gaiotto, but as far as I can see no explicit equation like the one above.