#10745: bug in elliptic curve gens()
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Reporter: rlm | Owner: cremona
Type: defect | Status: positive_review
Priority: major | Milestone:
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: Peter Bruin | Reviewers: Chris Wuthrich
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pbruin/10745-elliptic_curve_gens | 42c563c4b4e834adb39d75b3b02e21ab1c3da372
Dependencies: #10735 | Stopgaps:
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Comment (by pbruin):
Replying to [comment:24 wuthrich]:
> Well, I guess saturation (using the height pairing anyway) should filter
out the linearly dependent points too.
Actually the current patch at #8829 requires the initial points to be
linearly independent; it even has a doctest showing that it fails for
linearly dependent points... It is probably better to fix this ''after''
#8829, though.
> I was rather thinking of the other issue. Maybe a simple thing would be
to pass on the gens when using {{{base_extend}}}. The more advanced
"looking over smaller fields" seems too utopian.
OK, then I will open a ticket to fix at least the following (inspired by
the original problem):
{{{
sage: E = EllipticCurve([1,0,1,-1751,-31352])
sage: K.<d>=QuadraticField(5)
sage: E.gens()
[(52 : 111 : 1)]
sage: E.base_extend(K).gens()
[]
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/10745#comment:25>
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