# Tagged Questions

**5**

votes

**1**answer

484 views

### Main conjecture for elliptic curves

Suppose that $E$ is an elliptic curve defined over $\mathbb{Q}$, and that $p$ is a prime where $E$ has good ordinary reduction. Then one can define nonnegative integers $ \lambda_{E}^{alg} $, $ ...

**0**

votes

**1**answer

154 views

### Elliptic curves over $\mathbb{Q}$ with no rational torsion and $\mu$-invariant equal to 1 at $p=3$

How to find out examples over elliptic curves over $\mathbb{Q}$ with no rational torsion and $\mu$-invariant equal to 1 at $p=3$ $?$

**3**

votes

**1**answer

333 views

### $\mu$-invariant and Pontryagin dual of Selmer group of elliptic curves 2

Consider the elliptic curves -
$ E_{1}: y^{2}+y=x^{3}+x^{2}-769x-8470 $ $ [\text{Cremona}:19a2] $
$ E_{2}: y^{2}+xy+y=x^{3}-86x-2456 $ $ [\text{Cremona}:38a2] $
with both good ...

**3**

votes

**2**answers

184 views

### $\mu$-invariant and Pontryagin dual of Selmer group of elliptic curves 1

1) What are the examples of elliptic curves over $\mathbb{Q}$ with good reduction and $\mu$-invariant $\geq 2$ at $p = 3$ and how to find them $?$
2) Let $\Lambda = \mathbb{Z}_{p}[[T]] $ and $ ...

**2**

votes

**1**answer

306 views

### Invariants for isogenous elliptic curves

How to prove that for elliptic curves, the $\lambda$-invariant is always unchanged by an isogeny ?

**13**

votes

**3**answers

906 views

### rational points on algebraic curves over $Q^{ab}$

Motivation:
Let $Q_{\infty,p}$ be the field obtained by adjoining to $Q$ all $p$-power roots of unity for a prime $p$. The union of these fields for all primes is the maximal cyclotomic extension ...

**10**

votes

**2**answers

1k views

### Are Kato's zeta elements integral?

Let $E$ be an elliptic curve over $\mathbb{Q}$ and $T$ the $p$-adic Tate module of $E$. Kato's Euler system, constructed in the paper "P-adic Hodge theory and values of zeta functions of modular ...

**12**

votes

**1**answer

688 views

### P-adic L-functions of nonabelian twists of elliptic curves

Let $E$ be an elliptic curve and $\rho$ an Artin representation of $\operatorname{Gal}(\overline{\mathbb{Q}} / \mathbb{Q})$. Then there is a "twisted L-function" $L(E, \rho, s)$, corresponding to the ...

**16**

votes

**4**answers

1k views

### Does p-adic $L$- function determine the $L$ function

Let $E_1$ and $E_2$ be two Elliptic curve defined over $\mathbb Q$ . Let $p$ be an fixed given odd prime of $\mathbb Q$ at which both the curves have good ordinary reduction. Moreover p-adic ...