1

I read somewhere that it is not possible to have rational parametrization for elliptic curves. So there is possibility of the existence of rational parametrization for a 'part' of elliptic curve or which may just miss finite number of points on the curve?

ersh
  • 1,260
  • 2
    In that case the function field of the curve would be $\cong \overline{K}(x)$ and its genus would be $0$. – reuns Dec 06 '18 at 22:55
  • 1
    To expand on @reuns, you can’t get a rational parametrization of even the slightest part of an elliptic curve, so long as that part isn’t finite, of course. – Lubin Dec 07 '18 at 01:04
  • Got it. Thank you – ersh Dec 07 '18 at 15:19

0 Answers0