Rational points on elliptic curves over the rationals
Using ell2cover
The function ell2cover returns a basis of the set of
everywhere locally soluble 2-covers of the curve. A cover is
given by a pair [Q, M]. The 2-cover is given by the quartic
y2 = Q(x) and M is a map from the quartic to the curve.
Finding a point on the cover allows to find a point on the curve.
? E=ellinit([1,0,1,-32866776356,-2293423702808798]);
? ellrank(E)
%13 = [2,2,0,[[55989637/144,360928708609/1728]]]
The rank is 2 but we have only one point. We can try to find the
second point manually with ell2cover.