Derong Qiu

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math.NT2001

Mordell-Weil groups and Selmer groups of two types of elliptic curves

Derong Qiu, Xianke Zhang

Consider elliptic curves $E = E_{σ} : y^{2} = x (x + σ p) (x + σ q),$ where $σ = \pm 1,$ $p$ and $q$ are prime numbers with $p + 2 = q$ . (1) The Selmer groups $ S^{(2)}(E/{\mathbf{Q}}), S^{(ϕ)}(E…

math.NT1998

Explicit classification for torsion subgroups of rational points of elliptic curves

Derong Qiu, Xianke Zhang

The classification of elliptic curves E over the rationals Q is studied according to their torsion subgroups E_{tors}(Q) of rational points. Explicit criteria for the classificatio…