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There is this recent work "Adventures in Supersingularland" (Arxiv preprint: https://arxiv.org/pdf/1909.07779.pdf) in which several predictions are made about isogeny graphs of supersingular elliptic curves based on experimental data. I am not aware whether the claimed have been proven formally in the meanwhile (that is in the last two months), but I expect the investigation in the preprint to be fertile soil for further (more theoretical) research.