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2 years ago
gh-35626: Update the rank function of elliptic curves to use ellrank in pari ### :books: Description Fixes #35621 Pari has now a very good in-built algorithm to determine the rank and a set of generators of the Mordell-Weil group of elliptic curves over the rational. It is, as far as I understand, a port of Denis Simon's script ellQ.gp. It performs a 2-descent and uses the Cassels Tate pairing to conclude the rank in many cases - when Sha has no 4-torsion elements. The functionality to search rational points is also very quick. ### :memo: Checklist <!-- Put an `x` in all the boxes that apply. It should be `[x]` not `[x ]`. --> - `[x]` The title is concise, informative, and self-explanatory. - `[x]` The description explains in detail what this PR is about. - `[x]` I have linked a relevant issue or discussion. - `[x]` I have created tests covering the changes. - `[x]` I have updated the documentation accordingly. ### :hourglass: Dependencies - #35614 a pull request that fixes, among other things, the documentation in the files changed here. To avoid problems, I based it on that PR. <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: https://github.com/sagemath/sage/pull/35626 Reported by: Chris Wuthrich Reviewer(s): Chris Wuthrich, John Cremona, Lorenz Panny
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