Your curves may well have non-trivial Sha[2], which mwrank will not be able to deal with and which will result in only lower and upper bounds for the rank being obtained.
For example, in the second curve i nyour list (run with -p200, -h12 and -v2 so I could see what it was doing (recommended) I get the following: Generator 1 is [9867530972109845877120:-7172531151497870854932328320:10749963743]; height 19.923643512006684439379204763633354834654928208107068904746639317746846742994233588474225682335250773306984557783987616971435721195464716862694565438380981564520421643845041991597169415796134556914923 Generator 2 is [1229290048098:1119186226360006434:1]; height 6.6523079302033154488182993529491814791223497405644584954763805789805837726998970839794408966835376318890900887335114187391889127989088632717092020854375850283831708537108386945720005433860578159934535 Generator 3 is [30268150017653294105195118346767360:76124331356840241866944251800080107068928:4482995842509846743375]; height 49.547474666305922560644410161190091453155594912473038930510170319577836857003986094586253778271597533769968546078990514399018760153371368148377997174112339552112214820382460360031128525396290187327087 Generator 4 is [1192326947579269521269566634465921960134719450980449682:557295190238412987593301799213476879926557030950555213750550:2043491019135711717109440564508232963508373]; height 73.53352336975900462060382118607937612269796035971108483065842609752052519373428420261640865036646050278306892442444127401464798955033843905481345174553879349802927149963478900319193694770947194810527 Regulator = 20200.01809867956109151224905487983268871924073742494297569026377223593343264488344013131080669989819032090165496763712987054984046450454241529484791900452459958970523958903152452077137206880974020059 The rank has not been completely determined, only a lower bound of 4 and an upper bound of 6. If the rank is equal to the lower bound, the basis given is for the full Mordell-Weil group (modulo torsion). It is quite possible that the actual rank is 4, not 6. But the conductor is too large to be able to compute the analytic rank. If you want to know more about the 2-descent algorithm, refer to my book (http://www.warwick.ac.uk/staff/J.E.Cremona/book/fulltext/index.html)Chapter 3 and for the second descent some unpublished notes http://www.warwick.ac.uk/staff/J.E.Cremona/papers/d2.ps John Cremona 2011/7/30 raman kurdi <[email protected]>: > Dear Prof.Cremona > > Thnak you very mach > > I attached my curves that I can not compute their ranks > > Best Regards > Raman > > > On 7/28/11, John Cremona <[email protected]> wrote: >> On Jul 28, 9:32 am, raman kurdi <[email protected]> wrote: >>> Hi Dears >>> I have a family of elliptic curve that the number of this family is >>> 200000. >>> I want to compute the rank of this family and use the MWRANK program. >>> The option that I use is : -q -p 500 -v 0 >>> Unfortunately, for 60% of my curves MWRANK does not give an exact answer. >>> Could you please tell me is the above option correct? >>> Best >>> Raman >> >> Dear Raman, >> >> mwrank implements a method which cannot, even in >> principle,successfully compute the ranks of all elliptic curves over >> Q. >> >> Setting the flag -p500 (precision 500 decimals) is a good idea for >> curves with 2-torsion since it helps the reduction stage of a second >> descent. Another thing to set is -b (e.g. -b14) which controls how >> far to search for points on the homogeneous spaces -- but be warned >> (1) the maximum allowed is about 20, and (2) it's a logarithmic bound >> and increasing it by 1 is likely to increase the running time by >> exp(3/2). >> >> In any case the remark I made first is serious: if your curves have >> nontrivial Sha[2] and no 2-torsion then the method of 2-descent will >> find homogeneous spaces which have no rational points, but will be >> unable to prove that they have none. (That requires 4-descent which I >> only even implemented in Magma -- sorry!). >> >> Feel free to post a few of the curves which you difficulty with and >> I'll see if I can help. >> >> John Cremona (author of mwrank) >> >> -- >> To post to this group, send email to [email protected] >> To unsubscribe from this group, send email to >> [email protected] >> For more options, visit this group at >> http://groups.google.com/group/sage-support >> URL: http://www.sagemath.org >> > -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
