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
