I'm interested in plotting points of an elliptic curve over the real numbers. I'm looking to plot a few curves, but one like y^2 = x^3 + 7 would be an example of one. This is simple enough when x is positive, but when it's negative, I'm unsure how to find values. Are there any well-known algorithms for doing this?
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If you have, say $x=-2$, then your equation reads $y^2=-1$. That doesn't have any solutions. Is that what you're asking about? – Arthur Nov 22 '18 at 07:06
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1If you want points with real coordinates, it's simple enough to see when the right side is non negative, then for those $x$ a plus or minus squareroot gives the two $y values. – coffeemath Nov 22 '18 at 07:07
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1Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Nov 22 '18 at 07:07
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@Arthur right, that's true. I think what I'm struggling to wrap my head around is finding points of interest that do have solutions. For instance, how far back should I go before I know that there are no solutions anymore? – babaloo Nov 22 '18 at 07:16
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1You get a real point when $x^3+7\ge0$, that is iff $x\ge-\sqrt[3]7$. – Angina Seng Nov 22 '18 at 07:16
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Welcome to MSE! If you're familiar with programming, you can compute a list of points $(x,y)$ of the curve on your own. In view of the above curve, as Lord Shark said, real-valued points fulfill $x\geq -\sqrt[3]{7}$. Just loop over values $x$ and compute the $y$-values. Its easy with a computer algebra system like Maple.
Wuestenfux
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