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## Re: Mordell-Weil puzzle

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• ... Of course you are quite right, Jack. Brain not in gear :-( I was meaning: the rank is one, i.e. there is only one generator (and all other points are
Message 1 of 3 , Apr 7, 2013
--- In primenumbers@yahoogroups.com, Jack Brennen <jfb@...> wrote:
>
> The set of rational points is finitely generated, but there are definitely multiple rational points on this curve.
>
> Once you find one solution x,y, you can get more using PARI/GP:
>
> x=SOLUTION_X
> y=SOLUTION_Y
> e=ellinit([0,0,0,0,-6077])
> print(ellpow(e,[x,y],2))
> print(ellpow(e,[x,y],3))
> print(ellpow(e,[x,y],4))
> print(ellpow(e,[x,y],5))
>
> On 4/7/2013 1:18 PM, mikeoakes2 wrote:
> > Find a rational point on the curve
> > y^2 = x^3 - 6077
> >
> > Hint: there is exactly one.

Of course you are quite right, Jack.
Brain not in gear :-(

I was meaning: the rank is one, i.e. there is only one "generator" (and all other points are simply integral multiples of that, as per your code).

Mike
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