Integer points on elliptic curve

[Max Alekseyev]

On 10/19/07, Artur <grafix at csl.pl> wrote:
> Dear Seqfans,
> I  have question how find all integer solutions of elliptic curve
> a^2+/-1689b^2=c^3
> another than
> {a,b,c}={{41,1,-2},{3370,82,4}

First off, it is not a curve, it's a surface!
Second, there are infinitely many solutions, in particular, of the
form (a,b,c)=(xz,yz,z). For them the original equation is reduced to
x^2 +/- 1689 y^2 = z
that has solution for every pair of integers (x,y) (simply plug them
in and compute z).

> And question for MAGMA experts what mean parameters A in MAGMA  procedure:
> Sort([ p[1] : p in IntegralPoints(EllipticCurve([A, 1689])) ]);

You can look that up in online documentation.
http://magma.maths.usyd.edu.au/magma/htmlhelp/text1261.htm

Max



Are there any good resources out there for searching the web for equations?
I've suggested this once or twice on Google's public comments section.
Perhaps it's not a large enough subset of the searching public to warrant
putting in the effort. Anyways, I will often run across equations that seem
them. Being able to search effectively for these expressions would save me a
lot of time.