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Description
Currently we identify non-maximal ell-adic images of E/Q with potential CM by their projection to GL(2,Z/ell^nZ) from N_O(Z_ell), where N_O is the subgroup of GL_2(Zhat) defined in https://arxiv.org/abs/1809.02584v3, as explained in Section 12 of https://arxiv.org/pdf/2106.11141.
It is somewhat confusing that the link from the label of the ell-adic image takes you to the page for the modular curve corresponding to the inverse image of this group in GL(2,Zhat). It would be nice to instead have a knowl (and eventually perhaps a home page) for the inverse image in N_O; there is a tentative labelling scheme for these groups. At a minimum, it would be good to add a sentence to the Galois images section for PCM E/Q that explains what is going on here.