#11023: analytic_rank() should set rank() and gens() when it returns 0
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Reporter: weigandt | Owner: weigandt
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.7
Component: elliptic curves | Keywords: rank, gens
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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If the analytic rank of an elliptic curve over QQ is computed to be 0, it
is a theorem that the algebraic rank is 0, and we can set the generators
to be []. This is not done.
{{{
sage: E=EllipticCurve([1, 0, 0, -1319539461660, -159402536950172400])
sage: E.analytic_rank()
0
sage: E.rank()
Unable to compute the rank with certainty (lower bound=0).
This could be because Sha(E/Q)[2] is nontrivial.
Try calling something like two_descent(second_limit=13) on the
curve then trying this command again. You could also try rank
with only_use_mwrank=False.
---------------------------------------------------------------------------
BOOM!
RuntimeError: Rank not provably correct.
}}}
We could also set the rank to 1 if the analytic rank is provably 1, but it
seems customary only to set the rank when we can also set the generators,
so that shouldn't be done until improved Heegner point functionality is
available.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11023>
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