Let d be an integer and let K be a number field of degree d over Q. By the Mordell- Weil theorem we know that if E is an elliptic curve over K then there exist unique integers m, n > 0 and r \geq 0 such that E(K)_{tors} = Z/mZ x Z/mnZ x Zr as abelian groups.
Torsion points on elliptic curves over number fields of small degree / M. Derickx ; tutore: S.J. Edixhoven, P. Parent, L. Van Geemen ; coordinatore: L. Van Geemen. UNIVERSITA' DEGLI STUDI DI MILANO, 2016 Sep 21. 28. ciclo, Anno Accademico 2015. [10.13130/derickx-maarten_phd2016-09-21].
Torsion points on elliptic curves over number fields of small degree.
M. Derickx
2016
Abstract
Let d be an integer and let K be a number field of degree d over Q. By the Mordell- Weil theorem we know that if E is an elliptic curve over K then there exist unique integers m, n > 0 and r \geq 0 such that E(K)_{tors} = Z/mZ x Z/mnZ x Zr as abelian groups.
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