Timeline for Are most cubic plane curves over the rationals elliptic?
Current License: CC BY-SA 2.5
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| when toggle format | what | by | license | comment | |
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| Jul 29, 2019 at 3:36 | vote | accept | Idoneal | ||
| Jul 29, 2019 at 3:37 | |||||
| Feb 6, 2014 at 8:29 | answer | added | Chandan Singh Dalawat | timeline score: 14 | |
| Apr 23, 2010 at 12:56 | answer | added | Junkie | timeline score: 3 | |
| Jan 12, 2010 at 16:12 | comment | added | Felipe Voloch | Checking all curves with N=1000 is unfeasible. One could try to do a Monte Carlo test choosing a bunch of random curves in that range. But it is going to be hard to distinguish between positive, but small, density in the limit and a density that goes to zero like 1/log N. | |
| Jan 12, 2010 at 4:19 | history | edited | Idoneal | CC BY-SA 2.5 |
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| Jan 11, 2010 at 13:02 | history | edited | Jorge Vitório Pereira |
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| Jan 11, 2010 at 12:16 | history | edited | Idoneal | CC BY-SA 2.5 |
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| Jan 11, 2010 at 5:10 | history | edited | Idoneal | CC BY-SA 2.5 |
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| Jan 11, 2010 at 5:08 | comment | added | Idoneal | Is it possible to check this guess numerically? Say, with N= 1000, can one possibly get a lower bound on the number of such curves? | |
| Jan 11, 2010 at 5:02 | history | edited | Idoneal | CC BY-SA 2.5 |
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| Jan 11, 2010 at 4:48 | history | edited | Idoneal | CC BY-SA 2.5 |
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| Jan 11, 2010 at 4:40 | history | edited | Idoneal | CC BY-SA 2.5 |
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| Jan 10, 2010 at 21:30 | comment | added | Pete L. Clark | Along with Bjorn Poonen and Swinnerton-Dyer, I will guess that the answer is 0. (Of course I can't prove it either, although it is the sort of question I like to think about.) | |
| Jan 10, 2010 at 19:56 | comment | added | Ilya Nikokoshev | @Idoneal, I think the question about Zariski density is a bit different and may very well have known answer (intuitively, more likely to be yes). So I think you should post it separately. | |
| Jan 10, 2010 at 19:42 | answer | added | Felipe Voloch | timeline score: 9 | |
| Jan 10, 2010 at 17:55 | history | edited | Idoneal | CC BY-SA 2.5 |
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| Jan 10, 2010 at 17:41 | answer | added | Bjorn Poonen | timeline score: 24 | |
| Jan 10, 2010 at 17:40 | comment | added | Idoneal | Yes, this is a nice point. Let me add that I am not quite satisfied with the formulation of my question. I think clearing denominators is not a natural thing to do here. I wonder if the condition of having a rational point or not is a (Zariski) dense condition. – Idoneal 2 mins ago | |
| Jan 10, 2010 at 17:24 | comment | added | David E Speyer | Nice question! Let me point out something which confused me for a while, and might be confusing others. Any elliptic curve over Q can be embedded as a plane cubic with a rational flex. And I think it should be doable to show that almost all plane cubics over Q do not have rational flexes. However, this does not answer your question! These curves may still have rational points; it is just that they are not embedded in a way that puts those rational points at flexes. | |
| Jan 10, 2010 at 16:59 | history | asked | Idoneal | CC BY-SA 2.5 |