Rational points on elliptic curves over the rationals
Computing the full group
Even if the points found by ellrank have full rank, they might
generate a subgroup (of finite index) of the Mordell-Weil group.
The function ellsaturation attempts to obtain the full group
? E=ellinit([0,0,1,-7,6]);
? R=ellrank(E)
%22 = [3,3,0,[[-1,3],[-3,0],[11,35]]]
? S=ellsaturation(E,R[4],500)
%23 = [[1,-1],[2,-1],[0,-3]]
The number 500 means that we only check that no prime
p < 500 divides the index of the subgroup.