Timeline for Why are integer points on elliptic curves interesting and useful?
Current License: CC BY-SA 3.0
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| Nov 9, 2015 at 20:30 | comment | added | Joe Silverman | @Benjamin The technique being used to generate high rank also tends to produce lots of integer points. I would guess that they then just start taking subsets and computing the canonical height pairing matrices to find a set that is independent. My recollection is that Elkies rank 28 curve has well over 100 points with integer coords, so they're not all independent. Another favorite example of mine is $y^2=x^3+17$, which has rank 2 and has 8 pairs of integer points. | |
| Nov 9, 2015 at 17:30 | comment | added | Benjamin | Thanks a lot for this nice answer! What about the independence of integer points? I think there must be a way to show that two Points $P_1$ and $P_2$ are independent. For example you can find several rank record on this side: [this][1] side. I noticed that many generating points are integer points, so it seems the authors used some technique to show that the points are independent. [1]: web.math.pmf.unizg.hr/~duje/tors/rankhist.html | |
| Nov 7, 2015 at 18:55 | history | answered | Joe Silverman | CC BY-SA 3.0 |