1. ## elliptic torsion group

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

2. Originally Posted by zverik136
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