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The extension method is really designed for towers of finite fields.

To define a finite field as an extension of the prime field, one can use the GF or FiniteField constructor.

It can take an optional modulus argument:

sage: K.<a> = GF(2^1000, modulus=x^1000 + x^5 + x^4 + x^3 + 1)

For more information, read its documentation:

sage: GF?

or

sage: FiniteField?

The extension method is really designed for towers of finite fields.

To define a finite field as an extension of the prime field, one can use the GF or FiniteField constructor.

It can take an optional modulus argument:

sage: K.<a> = GF(2^1000, modulus=x^1000 + x^5 + x^4 + x^3 + 1)

For more information, read its documentation:

sage: GF?

or

sage: FiniteField?