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

Tomislav Gužvić; Bidisha Roy

doi:10.2478/auom-2022-0022

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 30 (2022): Issue 2 (May 2022)

By: Tomislav Gužvić and Bidisha Roy

Open Access

|Jun 2022

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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Articles in this issue

DOI: https://doi.org/10.2478/auom-2022-0022 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 125 - 132

Submitted on: May 12, 2021

Accepted on: Jan 24, 2022

Published on: Jun 2, 2022

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

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© 2022 Tomislav Gužvić, Bidisha Roy, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 30 (2022): Issue 2 (May 2022)