Rational points on elliptic curves over the rationals
ellrank
The GP function ellrank attempts to compute the rank of the
the Mordell-Weil group attached to a curve. This is based on
Denis Simon’s GP script for 2-descent and on Tom Fisher’s
algorithm for the Cassels pairing. The function returns
[r, R, s, L] such that the rank is between r and R (both
included), s is the rank of Ø[2]/2Ø[4] and L is a list of
independent, non-torsion rational points on the curve.
? E = ellinit([-289,1]);
? ellrank(E)
%2 = [5,5,0,[[-3,29],[-7,41],[-1,17],[-15,31]
% ,[-16,23]]]
Favorable case: the rank is 5 and a Q-basis is known.