### Elliptic Curve over Tower of Finite Field

So I was trying to construct a curve and compute arithmetics on different hierachy of extensions.
The problem is, since in my application the characteristic $p$ is so large that the regular `Fq.extension(degree)`

runs like forever. I'm not sure why but I could instead compute `irr = PolynomialRing(Fq,'x').irreducible_element(degree)`

and then just do the extension `extFq = Fq.extension(irr)`

by explicitly specifying a irreducible. However, my curve obtain by `E.change_ring(extFq)`

would no longer be recognized over finite field and able to sample a random point. Thus the following snippet fails

```
q, degree = 6441726727896377540006619567673100761, 8
# q is some priori decided prime power and degree is roughly 8
Fq = GF(q)
E = EllipticCurve(Fq,[1,0])
irr = PolynomialRing(Fq,'x').irreducible_element(degree)
extFq = Fq.extension(irr)
extE = E.change_ring(extFq)
extE.random_element() #this fails
```

On another hand, if I simply specify the relative extension `extFq = GF(q^degree)`

and use the relative extension `RelativeFiniteFieldExtension`

to get the embedding, then I'm not sure how to specify the coersion explicitly while using `E.change_ring`

.

~~q, ~~p, degree = 2538055698343985819, 8
p = q^2
Fq = GF(q)
E = EllipticCurve(Fq,[1,0])
irr = ~~PolynomialRing(Fq,'x').irreducible_element(degree)
~~PolynomialRing(GF(p),'x').irreducible_element(2*degree)
extFq = GF(q^degree,'x',irr)
# we could obtain embedding by
rel = RelativeFiniteFieldExtension(extFq,Fq)
E.change_ring(extFq) # error: no coersion

Is there any way to get around this?