Re: Help with an elliptic curve?

In article <1130928658.516047.173050@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<titus_piezas@xxxxxxxxx> wrote:

> Hello all,
>
> I need to solve the equation,
>
> y^2 = 20x^3-19x^2+14x-11
>
> where x,y are rationals.
>
> (P.S. It has small integer solutions at x=1,3 but any other rational
> point?)
>
>
You have 5 known rational points. In homogeneous coordinates they are
x:y:1 =
0, 1, 0
1, 2, 1
1, -2, 1
3, 20,1
3, -20,1

The line through two of these points will intersect the curve in
another rational point. (Bring scratch paper, and several sharp
pencils with good erasers.)

--
Chris Henrich
http://www.mathinteract.com
God just doesn't fit inside a single religion.
.

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