Disclaimer: Most (if not all) of these aren't open questions in the sense that they are unsolved in the literature/community at large (a list of the 'Isogeny Problems' can be found here). They are 'open' in the sense that I have yet answered them for myself either here or in general. They are also not ordered in any rational way. I will likely come back and update this page when questions have been answered (or are completely trivial for one reason or another).