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arXiv · 2105.04954

Torsion groups of Mordell curves over number fields of higher degree

Tomislav Gužvić·Bidisha Roy
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Abstract

Mordell curves over a number field $K$ are elliptic curves of the form $ y^2 = x^3 + c$, where $c \in K \setminus \{ 0 \}$. Let $p \geq 5$ be a prime number, $K$ a number field such that $[K:\mathbb{Q}] \in \{ 2p, 3p \}$ and let $E$ be a Mordell curve defined over $K$. We classify all the possible torsion subgroups $E(K)_{\text{tors}}$ for all Mordell curves $E$ defined over $\mathbb{Q}$ when $[K: \mathbb{Q}] \in \{2p, 3p \}$.

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Tomislav Gužvić, Bidisha Roy. 2021-05-11. Torsion groups of Mordell curves over number fields of higher degree. https://arxiv.org/abs/2105.04954

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