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Section Three-Descent, which concerns three descent on elliptic curves,
is relevant for studying rational points on plane cubics
(genus one models of degree 3) over the rationals.
A very efficient PointSearch for schemes is available;
for details see Section Searching for Points.
This will find all rational points up to absolute height H
on the curve associated to a given genus one model
in time O(H2/d), where d
is the dimension of the ambient projective space.
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