How to visualize an elliptic curve?

Question

Mathematics

An elliptic curve is given by the formula, for example

y2 = x3 - x + 1

Run poix by the formula

y = Convert::ToInt32(sqrt((double)(x*x*x + a*x + b)));

And we get something similar to a parabola



. How to achieve such a graph? As in Wikipedia



I can not understand Something.

Answer 1

Have you tried substituting a=-1, b=1 into your formula?
For x=-1, your formula will return y= 1.
Why it doesn't draw anything, I can't tell without seeing all of your code. Perhaps something breaks there because of the roots of negative numbers. Need to check first. that x^3+ax+b >= 0, and only in this case calculate y and draw points. And, yes, you need to loop through x from negative numbers too.
You can first solve the equation x^3+ax+b = 0 to understand the domain of the function.