how would one go about finding torsion groups over the rationals, for example:
$\displaystyle Y^2= X^3 + 1 $ or
$\displaystyle Y^2=X(X-1)(X+2)$
thank you.
Mazur's theorem narrows down the possibilities for $\displaystyle Tor_\mathbb{Q}(E)$ 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