Czechoslovak Mathematical Journal, first online, pp. 1-17


The torsion subgroup of a family of elliptic curves over the maximal abelian extension of $\mathbb{Q}$

Jerome Tomagan Dimabayao

Received February 25, 2019.   Published online April 2, 2020.

Abstract:  We determine explicitly the structure of the torsion group over the maximal abelian extension of $\mathbb{Q}$ and over the maximal $p$-cyclotomic extensions of $\mathbb{Q}$ for the family of rational elliptic curves given by $y^2 = x^3 + B$, where $B$ is an integer.
Keywords:  torsion group; elliptic curve; cyclotomic field
Classification MSC:  14H52, 11R18
DOI:  10.21136/CMJ.2020.0082-19

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Affiliations:   Jerome Tomagan Dimabayao, Institute of Mathematics, College of Science, University of the Philippines-Diliman, C.P. Garcia Ave, Diliman, Quezon City, 1101, Philippines, e-mail: jdimabayao@math.upd.edu.ph


 
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