# ag.algebraic geometry – The orders of \$mathbb{F}_{p^n}\$- ratinoal points of a fiexed abelian variety and MAGMA computation

Let $$A$$ be an abelian variety over $$mathbb{F}_p$$.
Then of course for every natural number $$i$$, we have that $$# A(mathbb{F}_{p^i})$$ divides $$# A(mathbb{F}_{p^{i+1}})$$.

But MAGMA says this is false:
Here is my code:

``````P<x> := PolynomialRing((FiniteField(3)));
J := Jacobian(HyperellipticCurve(x^6 - 2 * x^5 + x^4 - 2 * x^3 + 6 * x^2 - 4 * x + 1));
for j in (1..10) do;
Order(BaseChange(J, FiniteField(3, j)));
end for;
``````

And the result is:

19
57
1444
5529
59299
467856
4976347
43264425
394975876
3458495577

What is wrong?