A simple practical higher descent for large height rational points on certain elliptic curves

Details A simple practical higher descent for large height rational points on certain elliptic curves A simple practical higher descent for large height rational points on certain elliptic curves

1999-04-30

arxiv.org/abs/math/9904172v1

Mathematics

Number Theory

14 pages, Latex2e

Scientific paper

We consider the practical computation of rational points on y^2=x(x^2+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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