Infinitely many rational elliptic curves with 2-torsion over quadratic fields
Let ppp be a prime satisfying … For an elliptic curve E/QE/\mathbb QE/Q, write E(Q(−p))torsE(\mathbb Q(\sqrt{-p}))_{\mathrm{tors}}E(Q(−p))tors for its torsion subgroup over Q(−p)\mathbb Q(\sqrt{-p})Q(−p). Existence…