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"content": "yes, I myself very much view isogenies as the morphisms between elliptic curves (and I guess more generally between abelian varieties, but I know even less in that case). I believe the point is that one gets a 'dual' isogeny [1, Theorem 1] in the other direction, so _existence_ of an isogeny is (I think) an equivalence relation. But really one should consider the actual maps...\n\n[1] https://www.johannesloher.com/assets/files/the_dual_isogeny.pdf",
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