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Math Help - torsion group

  1. #1
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    Post 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.
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  2. #2
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    Quote Originally Posted by zverik136 View Post
    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
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