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

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}.

Keywords

• elliptic curves
• torsion group
• number fields
• primary: 11g05, 11r16, 11r21
• secondary: 14h52