You can do (attempt) etale descent over one of the quadratic number fields defined by any of the factors. See section 8.3 of my paper [Elliptic curves over $\mathbb Q$ and 2-adic images of Galois](https://arxiv.org/abs/1402.5997) with Jeremy Rouse for an example of how to do this (there is [code](https://arxiv.org/src/1402.5997/anc/2adic.rar) available on the arXiv too).