### Is there a way to check if a given Elliptic-curve in a finite field has an element with a certain $x$ value?

Hi, I already found out how to generate an elliptic curve in a finite field in sagemath. How to get its ~~oder ~~oder, an element and some more. E.g.

```
E = EllipticCurve(GF(43),[2,8]);
E.order();
E.gens();
E.random_element()
```

But is there a way to check if the EC contains a point with a given x-coordinate?

(which returns a point including the y-coordinate as well)

Or as alternative a function which searches for a point closest to a given x value.

(For small EC I could just search among all elements but target usage is an EC with very high order)