Graphically representing points on Elliptic Curve over finite field I have taken elliptic curve $E\colon y^2=x^3-4x+20$, defined over $\mathbb{F}_{29}$.
The number of points on the curve, $\left|E(\mathbb{F}_{29})\right|=37$.

I took base point $P=(1,5)$, and got following results:



I want the results graphically to know the behaviour of the curve.

Is there any tool for this to show results graphically by giving input as curve points?
None of the above answers see the mistake in the question. The point $P=(1,5)$ is not on the curve $E\colon y^2=x^3-4x+20$ over $\mathbb{F}_{29}$. To see this, place $x=1$ and $y=5$ into the curve equation.
\begin{align}
5^2&amp;=1^3-4+20\\
25&amp; = 1-4+20\\
25&amp; \neq 15\\
\end{align}
Therefore $P = (1,5)$ is not on the curve. But it is on the curve $E'\colon y^2=x^3\color{red}{+}4x+20$ over $\mathbb{F}_{29}$.
Now, let us continue to the second equation as $E \colon y^2=x^3\color{red}{+}4x+20$
The curve $E$ has 37 points; the below lists them in projective coordinates;
$[(0 : 1 : 0), (0 : 7 : 1), (0 : 22 : 1), \color{red}{P =(1 : 5 : 1)}, (1 : 24 : 1), (2 : 6 : 1), (2 : 23 : 1), (3 : 1 : 1), (3 : 28 : 1), (4 : 10 : 1), (4 : 19 : 1), (5 : 7 : 1), (5 : 22 : 1), (6 : 12 : 1), (6 : 17 : 1), (8 : 10 : 1), (8 : 19 : 1), (10 : 4 : 1), (10 : 25 : 1), (13 : 6 : 1), (13 : 23 : 1), (14 : 6 : 1), (14 : 23 : 1), (15 : 2 : 1), (15 : 27 : 1), (16 : 2 : 1), (16 : 27 : 1), (17 : 10 : 1), (17 : 19 : 1), (19 : 13 : 1), (19 : 16 : 1), (20 : 3 : 1), (20 : 26 : 1), (24 : 7 : 1), (24 : 22 : 1), (27 : 2 : 1), (27 : 27 : 1)]$
Visualizing a curve is easy when the curve is defined over the Rational Field.

Where all the arithmetic-geometric relation work almost flawlessly; that is $$P+Q-R$$ is on the same line;
When we turn in to finite field case, we have a discrete plot;

The blue line is drawn to show the symmetry since if $(x,y)$ satisfies a point therefore $(x,-y)$ ( in the plot $ = (x,29-y)$) also satisfies the equation.
Now we can see the point addition with $P=(1,5), Q=(5,7)$ and $R = P+Q = (16,2)$ is drawn on the figure.

The proof of the connection of this figure with the ECC point addition is performed by Fgrieu for this question : Must a line hitting two points on the elliptic curve over a finite field hit another point by continuation?
As we can see from these figures, the point of infinity is missing here. Consider the summation of $R$ and $-R$, there it should be $\mathcal{O}$ on the vertical line! nope!.
Another visualization is the Torus shape. Any rectangle image can be map into a torus shape.

This is a vector image with Asymptote and the points that cannot be seen directly are set to be opaque. This is calculated by ray-tracing. The $R$ and $-R$ on the background. This 3D can be best viewed within HTML. A snapshot from the bottom;

The HMTL is interactive, you can zoom and rotate in 3D, you can download it from Github and view it locally.