Changes between Initial Version and Version 2 of Ticket #11023
 Timestamp:
 Mar 25, 2011, 6:18:01 AM (12 years ago)
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Ticket #11023

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Summary
changed from
analytic_rank() should set rank() and gens() when it returns 0
toAdd proof=False and proof=True flags analytic_rank()

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Summary
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Ticket #11023 – Description
initial v2 7 7 0 8 8 sage: E.rank() 9 Unable to compute the rank with certainty (lower bound=0).10 This could be because Sha(E/Q)[2] is nontrivial.11 Try calling something like two_descent(second_limit=13) on the12 curve then trying this command again. You could also try rank13 with only_use_mwrank=False.14 15 9 BOOM! 16 17 10 RuntimeError: Rank not provably correct. 18 19 11 }}} 20 12 21 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. 13 I suppose because analytic_rank() returns an integer that is *probably* the analytic rank, not *provably* the analytic rank. For example: 14 15 {{{ 16 sage: EllipticCurve([0,0,1,7,36]).analytic_rank() 17 4 18 }}} 19 20 We should keep the current implementation under a flag of proof=False, and see how much can be said for proof=True. It seems like we should at least be able to prove that a curve of smallish conductor has analytic rank 0 without too much trouble.