Well the way I first tried is as follows:

age: F.<x>=GF(2)[]
sage: G.<a>=F.quotient(x^6 + x^4 + x^2 + x + 1)
sage: a.multiplicative_order()
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)


But it gives a not implemented error. Luckily the following does work:

sage: G.<a>=GF(2^6,modulus=x^6 + x^4 + x^2 + x + 1)
sage: a.multiplicative_order()
21

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