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
y^2=x^3-348535556161x^2+9411982512955600953600x [0,-348535556161,0,9411982512955600953600] y^2=x^3-432375947809x^2+39305500949380532025600x [0,-432375947809,0,39305500949380532025600,0] y^2=x^3-912408950401x^2+86586744854271550694400x [0,-912408950401,0,86586744854271550694400,0] y^2=x^3-536710086025x^2+59813703564011517306384x [0,-536710086025,0,59813703564011517306384,0] y^2=x^3-1855765930225x^2+26681224725077190456384x [0,-1855765930225,0,26681224725077190456384,0] y^2=x^3-1001898900601x^2+225104091544539413571600x [0,-1001898900601,0,225104091544539413571600,0] y^2=x^3-2423019126025x^2+37719046943947124807184x [0,-2423019126025,0,37719046943947124807184,0] y^2=x^3-2361732724849x^2+197833836741502151361600x [0,-2361732724849,0,197833836741502151361600,0] y^2=x^3-1946708610025x^2+339790269763746950924304x [0,-1946708610025,0,339790269763746950924304,0] y^2=x^3-920112600625x^2+89987080452485248355904x [0,-920112600625,0,89987080452485248355904,0] y^2=x^3-129897530569x^2+505788650855590611600x [0,-129897530569,0,505788650855590611600,0] y^2=x^3-190484238025x^2+8130585454709316664464x [0,-190484238025,0,8130585454709316664464,0]
