Timeline for Background for the Elkies-Klagsbrun curve of rank 29
Current License: CC BY-SA 4.0
3 events
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| Aug 30 at 15:50 | comment | added | Will Sawin | @SamHopkins I haven't heard of any such conjectures, and I believe there are none. The difficulty is that these heuristics are all based on probabilistic ideas, and (1) it's much easier to do probabilistic heuristics asymptotically instead of for elliptic curves of fixed size, which would be needed to understand the finitely many values, and (2) all a probabilistic heuristic would give you is the claim that the probability that there are elliptic curves of rank greater than $n$ is small, not that it's impossible, so you'd have to decide a cutoff "small enough" probability. | |
| Aug 30 at 15:40 | comment | added | Sam Hopkins | In the past ten years there has been work on heuristics for boundedness of ranks of elliptic curves, e.g., arxiv.org/abs/1602.01431. That paper in particular conjectures there are only finitely many elliptic curves of rank greater than 21. Do you know if anyone has conjectured a value of $n$ such that there are no elliptic curves at all of rank greater than $n$? | |
| Aug 30 at 15:34 | history | answered | Will Sawin | CC BY-SA 4.0 |