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Keywords:
torsion group; elliptic curve; cyclotomic field
torsion group; elliptic curve; cyclotomic field
Summary:
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.
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