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Identifying the curves depends on an isomorphism between the residue field generated by lbar and the finite field generated by i. There's two possible isomorphisms, so with one choice the first curve on top is isomorphic to the first curve at the bottom, while with the other choice it's isomorphic to the second curve at the bottom. The fields are not canonically isomorphic, so there's no preferred isomorphism.

In general, support for isomorphisms of finite fields is not great in Sage. I recommend you factor polynomials and identify factors by hand.