All Questions

Shoichi Kihara constructed a family of elliptic curves with Mordell–Weil group $\mathbb{Z}/6\mathbb{Z}\times\mathbb{Z}^3$ (generic rank at least 3) in 2006. Kihara's family produces a number of rank 8 ...

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,...

Suppose that we have a surface $X$ defined over a field $k$ (I am interested in $k$ being a number field) and an elliptic fibration $f: X \rightarrow \mathbb{P}^1$, i.e. $f$ is proper and almost all ...

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 $...

I'm looking for references that can justify to what extent is the following statement true: Statement. Let $X$ be a smooth geometrically integral curve over a number field $k$. Then the Brauer-Manin ...

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 $...