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Aug 18, 2023 at 16:52 vote accept Bogdan Grechuk
Aug 18, 2023 at 16:47 comment added Michael Stoll I would think so, yes. (Whether this is satisfying depends on whether you want a theoretical result or a practical algorithm.)
Aug 18, 2023 at 16:42 comment added Bogdan Grechuk Thank you. In your other answer, you gave a method for which you cannot prove that it will always work. However, in this answer you (and the abstract of the paper) are talking about ALGORITHM for a more general problem, hence for this problem, right? So, can I write "Theorem. There is an algorithm for computing all rational points on any curve of genus $g\geq 2$ and rank of the Jacobian 0", and refer to this paper for a proof?
Aug 18, 2023 at 16:09 history answered Michael Stoll CC BY-SA 4.0