       Plot of Elliptic Curve with Grid

• To: mathgroup at smc.vnet.net
• Subject: [mg51512] Plot of Elliptic Curve with Grid
• From: "flip" <flip_alpha at safebunch.com>
• Date: Wed, 20 Oct 2004 01:21:52 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

I would like to plot an elliptic curve over Fp of the form:

y^2 = x^3 + ax + b (1)

I would then like to plot the list of points that satisfy (1).  {Note: I
have a way to generate that list).

I would like the continuous plot (like using implicit plot over reals) of
(1) with a grid having points of intersection over Fp (the integer points)
shown on the plot (over a grid).

Example:

y^2 = x^3 + 2x + 1 over F5

This curve has 7 points (counting the point at infinity).

The list of points is: S = {{0,1},{0,4},{1,2},{1,3},{3,2},{3,3}}

I would like to show a grid plot with the elliptic curve (continuous over
reals) superimposed over the discrete points given above (with points of
intersection (a dot of some sort shown for each point above)).

I would like to be able to pass in the "a, b, S" and have this automatically
generate the plot.

Is this easy?

Thanks for any input, Flip

****email****         flip         %%%%     @    %%%%%
nethere......com****************

Sorry for the crypto in my email, but spam is a killer

```

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