bash-2.03$ mwrank -b 13 -c 13 Program mwrank: uses 2-descent (via 2-isogeny if possible) to determine the rank of an elliptic curve E over Q, and list a set of points which generate E(Q) modulo 2E(Q). and finally search for further points on the curve. For more details see the file mwrank.doc. For details of algorithms see the author's book. Please acknowledge use of this program in published work, and send problems to John.Cremona@nottingham.ac.uk. Version compiled on Feb 9 2003 at 07:38:49 by GCC 3.2.1 using base arithmetic option LiDIA_ALL (LiDIA bigints and multiprecision floating point) Using LiDIA multiprecision floating point with 15 decimal places. Enter curve: [0,0,0,-1063395,-422075394] Curve [0,0,0,-1063395,-422075394] : No points of order 2 Basic pair: I=3190185, J=11396035638 disc=-10407740544 2-adic index bound = 2 By Lemma 5.1(b), 2-adic index = 1 2-adic index = 1 One (I,J) pair *** BSD give two (I,J) pairs Looking for quartics with I = 3190185, J = 11396035638 Looking for Type 3 quartics: Trying negative a from -1 down to -595 (-3,4,891,-594,-66366) --nontrivial...locally soluble...(x:y:z) = (211715 : 9349897 : 16886) Point = [52175045206724521444271926 : -13180351117189258356213783626 : 817373361745081357273] height = 43.1750544881976 Rank of B=im(eps) increases to 1 (-33,42,873,-564,-5952) --trivial (-105,-24,891,102,-1896) --trivial (-297,-270,801,392,-626) --trivial (-297,522,549,-684,-510) --trivial (-372,-141,873,168,-528) --trivial (-474,51,891,-48,-420) --trivial Finished looking for Type 3 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 Rank = 1 Points generating E(Q)/2E(Q): Point [52175045206724521444271926 : -13180351117189258356213783626 : 817373361745081357273], height = 43.1750544881976 Height Constant = 7.05593519484936 Max height = 43.1750544881976 Bound on naive height of extra generators = 11.8531634713158 After point search, rank of points found is 1 Generator 1 is [52175045206724521444271926 : -13180351117189258356213783626 : 817373361745081357273]; height 43.1750544881976 The rank and full Mordell-Weil basis have been determined unconditionally. Regulator = 43.1750544881976 (279 seconds) Enter curve: [0,0,0,0,0] bash-2.03$