It is known that e(k) is a nitely generated abelian group, and that for a given p, there is a nite, e ectively calculable, list of possible torsion subgroups which can appear. Let k denote the quadratic field q(d) where d=−1 or −3 and let e be an elliptic curve defined over k This is the biggest subgroup that only contains torsion elements
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My question is if we can find also a maximal subgroup that only contains torsion free elements.
Let e be an elliptic curve over q
About this article cite this article kamienny, s On the torsion subgroups of elliptic curves over totally real fields It enables us to classify the groups that can be realized as the torsion subgroup e(l)tors, by using the classification of torsion subgroups over the quadratic fields.
