#10745: bug in elliptic curve gens()
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Reporter: rlm | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone:
Component: elliptic curves | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by cremona):
The output of simon_two_descent() for EK is
{{{
sage: FK.simon_two_descent()
(1, 1, [])
}}}
which can be interpreted as follows: he computes the 2-Selmer rank is 1,
which gives a valid upper bound for the rank (=1). He fails to find
points on 2-coverings, so there are no points returned. *But* he uses the
parity conjecture to increase the lower bound from 0 to 1.
So when we decide (in the simon_two_descent()) method) that the output is
certain, we need to take this into account.
Secondly, the gens() function for curves over number fields is completely
reckless:
{{{
lower,upper,gens =
self.simon_two_descent(verbose=verbose,lim1=lim1,lim3=\
lim3,limtriv=limtriv,maxprob=maxprob,limbigprime=limbigprime)
return gens
}}}
There is no caching, no checking of Proof, and worst of all, the gens
which are returned have not been looked at at all. Just about all you can
say about them is that they are points on the curve.
Who let that in? This function needs changing urgently.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10745#comment:2>
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