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A remark on the torsion subgroups of elliptic curves

✍ Scribed by Jasbir Singh Chahal


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
138 KB
Volume
115
Category
Article
ISSN
0022-4049

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✦ Synopsis


of the torsion subgroup of E(K), the group of K-rational points on an elliptic curve E defined over a number field k, with K quadratic over k.


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Torsion subgroups of elliptic curves in
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Let E be an elliptic curve over Q and let F := Q({ √ m ; m ∈ Z}). Laska and Lorenz showed that there exist at most 31 possibilities for the type of the torsion subgroup E(F ) tors of E over F. In this paper, we showed that there exist exactly 20 possibilities for E(F ) tors .

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