#15299: Incorrect results for analytic Sha due to low precision
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Reporter: jdemeyer | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.13
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by pbruin):
Replying to [comment:22 cremona]:
> You can go one step further thanks to Gross-Zagier: if the parity is
odd and L'(1) looks zero then you can prove it, since if in fact L'(1)!=0
then the curve would have rank 1, but you can disprove that by finding
three (or oeven only 2) independent points.
That is true (in fact I seem to remember learning this from the talk you
linked to). However, it does require you to search for points; there
seems to be no "analytic" way of proving that L'(1) = 0 by computing it to
finite precision, like the `L1_vanishes()` function.
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Ticket URL: <http://trac.sagemath.org/ticket/15299#comment:23>
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