All Questions

Suppose we have an elliptic curve $E$ over $K$, an $l$-adic field. Say that $|j(E)|>1$ where $|.|$ is the $l$-adic valuation. By the theory of the Tate curve $E$ is isomorphic over $L$ to a Tate ...

I read an article where it is said: $E_1(\mathbb{Q}_p)\cong \mathbb{Z}_p$ where $E$ is an elliptic curve over $\mathbb{Q}_p$ and $E_1(\mathbb{Q}_p)=\{P\in E(\mathbb{Q}_p):\tilde{P}=\tilde{O}\}$. The ...

Let $K$ be an imaginary quadratic field and let $F$ be a finite extension of $K$. Let $E$ be an elliptic curve over $F$ with CM by $K$. Suppose that $p$ is a prime that splits as $p=\pi\pi^*$ in $K$. ...

Let $E/ \Bbb{Q}_p$ be an elliptic curve over $ \Bbb{Q}_p$. $\hat{E}$ denote the corresponding formal group of $E$. I want to prove $\Bbb{Q}_p(E[p])＝\Bbb{Q}_p(\hat{E}[p])$. $ \hat{E}[p]$ denotes $p$ ...

Let $E$ be an elliptic curve on $\Bbb Q_p$. $E_0(\Bbb Q_p)$ is points of $E(\Bbb Q_p)$ reduced to nonsingular points. How to prove #$E(\Bbb Q_p)$＝$∞$ directly ? According to Silverman's book 'the ...

Let $E/ \Bbb{Q}_p$ be an elliptic curve over $ \Bbb{Q}_p$. $\hat{E}$ denote the corresponding formal group of $E$. I want to know what $\Bbb{Q}_p(\hat{E}[p])/\Bbb{Q}_p$ is . At first I tried to prove ...