Torsion subgroups of rational Mordell curves over some families of number fields

Gužvić, Tomislav; Roy, Bidisha

doi:10.2478/auom-2022-0022

Abstract

Mordell curves over a number field K are elliptic curves of the form y² = x³ + c, where c ∈ K \ {0}. Let p ≥ 5 be a prime number, K a number field such that [K : ℚ] ∈ {2p, 3p}. We classify all the possible torsion subgroups E(K)_tors for all Mordell curves E defined over ℚ when [K : ℚ] ∈ {2p, 3p}.

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Torsion subgroups of rational Mordell curves over some families of number fields

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