#8496: Implement canonical heights for elliptic curves over number fields
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Reporter: robertwb | Owner: was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.3.4
Component: elliptic curves | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by robertwb):
Replying to [comment:11 wuthrich]:
> I have put up a rebased patch with a few minor changes. But I have not
included yet the documentation on the normalization. You write "THE BSD
formula", but there is not a unique standard way of stating the
conjecture, I fear. Also the question is whether or not you divide the
height pairing by two or not. Could you clarify this ?
OK, I have expanded the normalization section, borrowing heavily from the
explanation found in John Cremona's book.
> I deleted the assumption that E was defined over Q. I don't think you
will need that. Maybe it is needed that the model is integral, but I do
not see where you would require the curve to be defined over Q. Please
correct me if I am wrong.
Yes, you are correct. (There are examples to this effect.)
> By the way the diff of our two patches comes mainly from converting tabs
to spaces.
They were not of my doing, but thanks for expunging them.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8496#comment:12>
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