please explain how to show that $\displaystyle E(\mathbb{Q})[4] $ is a group of order at most 8.

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- Oct 31st 2009, 02:45 PMzverik136elliptic torsion group
please explain how to show that $\displaystyle E(\mathbb{Q})[4] $ is a group of order at most 8.

- Oct 31st 2009, 03:46 PMtonio

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

(i) A cyclic group of orderN 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