I seem to have run across a potential bug on Sage:

p = previous_prime(2^64)
> F.<x> = GF(p^2)
> x * 2**63
>
>
throws a "overflow in t_INT-->long assignment" exception creating the 
element x * 2**63. Reproduced here:

https://sagecell.sagemath.org/?z=eJwrULBVKChKLcvMLy2OLyjKzE3VMIozM9Hk5XLTs6mwA8q6u2kUxBkBBSq0jLS0zIwBihANsg==&lang=sage

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