# Tagged Questions

For questions regarding elliptic curves. Questions on ellipses should be tagged [conic-sections] instead.

0answers
31 views

### Galois action on the fibre of a morphism determined by a linear system

If $X$ is an elliptic curve, let $P,Q\in X$, then $|P+Q|$ determines a morphism $g:X\to \mathbb{P}^1$. It is easy to see $K(X)/K(\mathbb{P}^1)$ is a Galois extension of degree 2. Let $\sigma$ be the ...
1answer
70 views

### Does there have to be a point on elliptic curve over $\mathbb{C}(t)$

Let $E$ be an elliptic curve over $\mathbb{C} (t)$ (rational functions). I require $E$ to be defined by the following equation. $$y^2 = x^3 + A x + B$$ Where $A, B \in \mathbb{C} (t)$. Question: ...
2answers
68 views

### Diophantine equation resembling FLT

I was wondering if the equation $x^p+y^p=2z^p$ has been studied. For small cases it is seen that the only solutions are trivial: $x=y=z$. There are probably methods to solve this for regular ...
1answer
123 views

0answers
58 views