A simple practical higher descent for large height rational points on certain elliptic curves
Abstract
We consider the practical computation of rational points on y2=x(x2+ax+b). The algebra necessary for a 4-descent procedure is described. A simple further descent is then described which only uses integer arithmetic. Numerous examples are given to illustrate the effectiveness of this extra descent. Currently, the largest point found has height 51.15 or 102.3, depending on which height normalisation you use.
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