Rational points on elliptic curves over the rationals
Computing the full group
? r1=matdet(ellheightmatrix(E,R[4]))
%24 = 3.7542920288254557283540759015628405708
? r2=matdet(ellheightmatrix(E,S))
%25 = 0.41714355875838396981711954461809339675
? r1/r2
%26 = 9.0000000000000000000000000000000000000
We have found a group which is 3 times larger.