Ax, James The elementary theory of finite fields. Ann. of Math. (2) 88 1968 239–271.

I was wondering whether there is a ring isomopphism $\prod_p\mathbb{F}_p/\bigoplus \mathbb{F}_p\approx \prod_p \mathbb{F}_{p^p}/\bigoplus \mathbb{F}_{p^p}$ if we don't assume continuum hypothesis. Probably this theorem or is not mandatory to prove the decidability result even if CH is assumed. But it would be nice to know why this does/doesn't hold if CH is not assumed.

Okay. But how can I prove those are the only one? Am I right that the priviledged rational point is not an integer point?

Unfortunately the curve I had on my mind has larger conductor than 130000

Thanks! I have one curve which is of rank 4 and torsion subgroup isomorphic to trivial abelian group so I would like to know some method to prove the solutions I found are the only one.