| Abstract:
A fundamental theorem of L. J. Mordell says that the group of all
rational points in an elliptic curve is finitely generated. Recall
that a point P is called a torsion point if the sequence
{P, 2P, 3P, 4P,...}
terminates i.e. P is of finite order and its order is equal to the
smallest n > 0 such that nP = infinity, the identity of the group
law. By Mordell's theorem, there are only finitely many such points.
In this talk, we go through some well-known number-theoretic
algorithms to find all such points of a given curve. In this context,
a beautiful theorem of Barry Mazur says that an elliptic curve
defined over rationals can have at most 15 torsion points. In
particular, no elliptic curve has a rational point of order 11. Also,
for each n < 11 or n = 12, there are elliptic curves with a rational
point of order n. We produce a list of such curves.
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