engleski

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

Klasificirali smo sve torzijske grupe Mordellovih krivulja nad poljima algebarskih brojeva stupnja 2p i 3p, gdje je p prost broj. 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 group, Elliptic curves

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