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?
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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