<abstract xmlns="http://www.w3.org/1999/xhtml">

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

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Torsion subgroups of rational Mordell curves over some families of number fields"}

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...

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

Published Online: Jun 02, 2022

Page range: 125 - 132

Received: May 12, 2021

Accepted: Jan 24, 2022

DOI: https://doi.org/10.2478/auom-2022-0022

Keywords
Elliptic curves, Torsion group, Number fields

© 2022 Tomislav Gužvić et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Jun 02, 2022

Page range: 125 - 132

Received: May 12, 2021

Accepted: Jan 24, 2022

DOI: https://doi.org/10.2478/auom-2022-0022

KeywordsElliptic curves, Torsion group, Number fields

© 2022 Tomislav Gužvić et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Elliptic curves, Torsion group, Number fields