Rational points on elliptic curves over the rationals
ellrank
? E = ellinit([-127^2,0]);
? ellrank(E)
%5 = [1,1,0,[]]
Here the rank is 1 but no point is known. We can find the point
either with ellheegner (if the conductor is small enough) or
by asking ellrank to insist by setting the effort parameter to a
moderate value.
? ellheegner(E)
%6 = [-38749202011873484470143/306317326339867638016
% 678721624672968530804232808604865/5361142413550
? ellrank(E,5)
%7 = [1,1,0,[[611429153205013185025/9492121848205441
% 15118836457596902442737698070880/92479390070059