Steps To Reproduce

Launch the following script:

K = GF(4)
A.<x> = K[]
L = K.extension(x+1)
print("It is", L.is_field(), "that L is a field")
print("It has cardinality", L.cardinality())
print("Sage says that it is", L.is_prime_field(), "that L is a field of prime cardinality")
print("This is because L.degree() =", L.degree())

Expected Behavior

You would expect L.is_prime_field() to be False.

Actual Behavior

It is True that L is a field
It has cardinality 4
Sage says that it is True that L is a field of prime cardinality
This is because L.degree() = 1

Additional Information

As a remark, I feel it is dangerous that the method degree can have different meanings for finite fields depending on how they were created.

Environment

• OS: Debian 12.11
• Sage Version: SageMath version 10.7.beta8, Release Date: 2025-07-06

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide