Rational points on elliptic curves over the rationals
ellrank
? E = ellinit([1,0,0,-150752,-22541610]);
? [r,R,s,L]=ellrank(E,1)
%9 = [1,3,0,[[-136433699/608400,53209293359/47455200
Here the rank is either 1 or 3 and one point is known. Here the
conductor is small so we can check the analytic rank:
? A=ellanalyticrank(E)
%10 = [1,11.564255722521984467602889781900189064]
We find that the analytic rank is 1 so the rank is 1 and we have
a Q-basis.
? A[2]/ellbsd(E)/ellheight(E,L[1])
%11 = 16.000000000000000000000000000000000000