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We are writing a paper on the ranks of elliptic curves over cubic fields. The curves of different torsion subgroups are created by the formulas in Jeon et al. and by our new parametrizations. D. Jeon,...

This question could be related to my old and Duality's newer questions. I am building a $\mathbb{Z}/9\mathbb{Z}$ elliptic curve $E$ over $\mathbb{Q}$: $$E: y^2+(t^3-3t^2+1)xy + t^3(t-1)^3y=x^2$$ For $...

Question. Is it possible for an elliptic curve $E$ over quadratic field $K$ to have two separate (yet connected) isogeny classes? There are two $\mathbb{Z}/14\mathbb{Z}$ elliptic curves, $E_1$ and $...