# Math Help - torsion group

1. ## torsion group

how would one go about finding torsion groups over the rationals, for example:
$Y^2= X^3 + 1$ or

$Y^2=X(X-1)(X+2)$

thank you.

2. Originally Posted by zverik136
how would one go about finding torsion groups over the rationals, for example:
$Y^2= X^3 + 1$ or

$Y^2=X(X-1)(X+2)$

thank you.

Mazur's theorem narrows down the possibilities for $Tor_\mathbb{Q}(E)$ to a very few possibilities, and then you may try using Nagell-Lutz's Theorem to find some torsion points with integer entries.

You may also try to read the following http://www.math.ucla.edu/~burhanud/p...ion_paper2.pdf

Tonio