On Wed, 29 Nov 2006 12:25:14 -0800, Iftikhar Burhanuddin <[EMAIL PROTECTED]> wrote: >> On Wed, 29 Nov 2006 09:57:06 -0800, Enrique Acosta >> <[EMAIL PROTECTED]> wrote: >> > I tried it both on my computer and on the online SAGE notebook (the >> > worksheet called 0 is unlocked), and it crashes on both. > > On the SAGE command line E.rank() doesn't crash, it just raises a > NotImplementedError exception --- not sure why.
It's a bug on my part -- it really should crash :-) > Hope the following helps. All computations were run on sage.math > > Ifti. > > ps: You have a curve with rank >= 8! > pps: two_descent_simon is da bomb! Wow, it did it?! Excellent! I think that two_descent_simon computes the 2-selmer groups, so the rank is provably at most 8 (modulo it using PARI which assumes GRH+ by default). Thus that it found 8 independent points means it is exactly 8. By the way, I think two_descent_simon could do much more than what is exposed in SAGE -- i.e., it can do computations over number fields, and also do things with curves that have rational 2-torsion. I have for a long long time been looking for somebody to improve SAGE's use of two_descent_simon (which is a wrapper of a PARI program that I got Simon to GPL). Any volunteers? > ==== > sage: E = EllipticCurve([0, -285193/512, 0, 10272094875/131072, > -115889280609375/268435456]) > > sage: EM = E.minimal_model() > > sage: time EM.two_descent_simon() > > CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s > Wall time: 426.37 > > (8, > 8, > [(-1215132 : 10275255000 : 1), > (2024405508/3481 : 1399019017725000/205379 : 1), > (110215236/25 : 157858782984/125 : 1), > (-42363243528/18769 : 29469850310821680/2571353 : 1), > (177996328/121 : 5817722755600/1331 : 1), > (80882233177/17689 : 5728840955768125/2352637 : 1), > (2169480 : 1534252752 : 1), > (-2550336 : 11672417520 : 1)]) > > > From two_descent's documentation: > > "... > > NOTE: The points are not translated back to self only because I haven't > written code to do this yet. > ..." Volunteers?! :-) > > > ====================================== > The two_descent method invokes mwrank. > > On the original model two_descent terminates but I'm not sure what to > make of the output. > > sage: time E.two_descent() > Basic pair: I=76257, J=-34430400 > disc=588325044426372 > 2-adic index bound = 2 > 2-adic index = 2 > Two (I,J) pairs > Looking for quartics with I = 76257, J = -34430400 > Looking for Type 2 quartics: > Trying positive a from 1 up to 79 (square a first...) > Trying positive a from 1 up to 79 (...then non-square a) > Trying negative a from -1 down to -21 > Finished looking for Type 2 quartics. > Looking for Type 1 quartics: > Trying positive a from 1 up to 100 (square a first...) > Trying positive a from 1 up to 100 (...then non-square a) > Finished looking for Type 1 quartics. > Looking for quartics with I = 1220112, J = -2203545600 > Looking for Type 2 quartics: > Trying positive a from 1 up to 317 (square a first...) > Trying positive a from 1 up to 317 (...then non-square a) > (89,-140,-978,2100,-579) --nontrivial...locally soluble...(x:y:z) > = (-49 : 18283 : 10) > Point = [5519704840404938:-114647772666259630:6111423471187] > height = 26.249770150564216044299105711607770697196854030312 > Doubling global 2-adic index to 2 > global 2-adic index is equal to local index > so we abort the search for large quartics > Rank of B=im(eps) increases to 1 > Exiting search for large quartics after finding enough globally soluble > ones. > Looking for Type 1 quartics: > Trying positive a from 1 up to 403 (square a first...) > Trying positive a from 1 up to 403 (...then non-square a) > Finished looking for Type 1 quartics. > Mordell rank contribution from B=im(eps) = 1 > Selmer rank contribution from B=im(eps) = 1 > Sha rank contribution from B=im(eps) = 0 > Mordell rank contribution from A=ker(eps) = 0 > Selmer rank contribution from A=ker(eps) = 0 > Sha rank contribution from A=ker(eps) = 0 > CPU times: user 1.91 s, sys: 0.00 s, total: 1.91 s > Wall time: 1.91 > > > ====================================== > Two_descent on the minimal model hasn't completed as yet. > > sage: EM.two_descent() > Basic pair: I=78809911996, J=-38197235343608588 > disc=498925368345172860180530043750000 > 2-adic index bound = 2 > After 2-adic refinement (case 1); 2-adic index = 2 > 2-adic index = 2 > Two (I,J) pairs > Looking for quartics with I = 78809911996, J = -38197235343608588 > Looking for Type 2 quartics: > Trying positive a from 1 up to 82645 (square a first...) > (1,0,-3610947932,118112251884750,-1086578740733763719) > --nontrivial...(x:y:z) = > (1 : 1 : 0) > Point = [2407298621:118112251884750:1] > height = 16.321496267498527535905399749860055852097312312975 > Rank of B=im(eps) increases to 1 > > (1,0,-574346060,7492444623342,-27489443152300967) > --nontrivial...(x:y:z) = > (1 : 1 : 0) > Point = [382897373:7492444623342:1] > height = 16.041343458676659090742200454054250418256469900583 > Rank of B=im(eps) increases to 2 > (1,0,-4470236,5137208370,-1658683331975) --nontrivial...(x:y:z) = > (1 : 1 > : 0) > Point = [2980157:5137208370:1] > height = 11.196782508525490806554970385438002826340043215484 > Rank of B=im(eps) increases to 3 > (1,0,-957080,494380698,-69766017867) --nontrivial...(x:y:z) = (1 : 1 > : 0) > Point = [638053:494380698:1] > height = 12.718590453229143759444773755133553887696114482461 > Rank of B=im(eps) increases to 4 > (1,-1,-1509851,998153865,-183652882650) --nontrivial...(x:y:z) = (1 : 1 > : 0) > Point = [8052538:7979191515:8] > height = 12.261589901149609917240226853306431110996268789891 > Rank of B=im(eps) increases to 5 > > ================================= > > On Magma Rank(E) and TwoDescent(E) are still running and haven't printed > anything on screen. > > > > --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
