I am interested in the congruent number problem which involves finding a rational solution to
This equation is currently unsolved and many have tried. This equation gives the X and the Y values.
However I have a second equation which I believe also must be rational for a solution to exist which is in a different form and not cubic at all. My equation does not give X and Y but rather it gives the D which needs to be multiplied to X and Y to produce an integer triplet where X,Y,Z are all integers.
Once D is known I have a different method to efficiently solve for X,Y,Z.
Where would I look to find the tools to solve 4th order polynomial equations for rational solutions?
My equation is of the form:
$$(c^2)( v^4) - (6 c)( v^2) +1 =k^2$$
$c$ is a constant given to us.
$V$ and $k$ need to be rational.
Is this easier or harder than a 3rd order equation? Where should I look for the tools to solve this?
Thanks for any help.