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25029Re: Mordell-Weil puzzle

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  • mikeoakes2
    Apr 7, 2013
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      --- 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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