Opened 11 years ago

Last modified 7 years ago

#11023 new enhancement

analytic_rank() should set rank() and gens() when it returns 0 — at Initial Version

Reported by: weigandt Owned by: weigandt
Priority: major Milestone: sage-6.4
Component: elliptic curves Keywords: rank, gens
Cc: cremona, was Merged in:
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Report Upstream: N/A 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()
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.

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.

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