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Thread: elliptic torsion group

  1. October 31st 2009, 02:45 PM #1
    zverik136
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    elliptic torsion group

    please explain how to show that E(\mathbb{Q})[4] is a group of order at most 8.
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  2. October 31st 2009, 03:46 PM #2
    tonio
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    Quote Originally Posted by zverik136 View Post
    please explain how to show that E(\mathbb{Q})[4] is a group of order at most 8.

    Use Mazur's Theorem: the torsion group of non-singular elliptic curve over \mathbb{Q} has one of the following forms

    (i) A cyclic group of order
    N with 1 ≤ N ≤ 10 or N = 12.

    (ii) The product of a cyclic group of order two and a cyclic group of order     2N

    with 1 ≤ N ≤ 4.
    Tonio
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