On Thursday, July 28, 2011, Jack Fearnley wrote:
> I read in the help that heights have only been implemented for elliptic
curves over the rationals. My research involves computing heights of
algebraic points on elliptic curves and I have been using Magma for this.
>
> A colleague of mine claimed that Sage could compute heights over number
fields and demonstrated with example 2 from Siverman's 1988 paper*
>
> I confirmed this on my Sage (version 4.6.2) and also successfully
reproduced example 1.
>
> Suitably encouraged, I attempted to compute some heights on E37b over a
cyclic cubic extension and failed with error messages.
>
> Is anyone working on implementing this functionality?
> Can anyone explain why Silverman's examples work?
>
My understanding is that heights over number fields are fully implemented in
Sage and have been for *years*. What doc says otherwise? What exactly
fails? Post an exact session.
> Best wishes,
> Jack Fearnley
>
> * Computing Heights on Elliptic Curves
> Math. Comp. vol 51 No 183 (Jul 1988) pp 339-358
> http://www.jstor.org/pss/2008597
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--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
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