Changes between Version 4 and Version 10 of Ticket #10735


Ignore:
Timestamp:
Feb 15, 2014, 12:56:54 PM (9 years ago)
Author:
Peter Bruin
Comment:

Changing the documentation does indeed sound like the right solution here. The correctness of the parity of this upper bound probably relies on finiteness of Ш, or doesn't it?

Legend:

Unmodified
Added
Removed
Modified
  • Ticket #10735

    • Property Summary changed from Simon 2-descent may not check for solubility at archimedean places. to Simon 2-descent only returns an upper bound on the 2-Selmer rank
    • Property Dependencies changed from to #11005
    • Property Milestone changed from sage-5.12 to sage-6.2
  • Ticket #10735 – Description

    v4 v10  
    44
    55Sometimes the second entry is larger than the actual 2-Selmer rank as computed by mwrank, and predicted by BSD. The first curve I know of for which this happens is the elliptic curve '438e1' from Cremona's tables.
    6 
    7 This curve definitely possesses 2-covers which are everywhere locally soluble EXCEPT at that infinite place. These probably explain the discrepancy.
    86
    97{{{
     
    16141
    1715}}}
     16
     17The explanation for this is that `E.simon_two_descent()`, unlike Cremona's `mwrank`, does not do a second descent and therefore only determines an upper bound on the 2-Selmer rank.