I got this from the "report a problem" bug submission form:
The selmer_group() method of a number field works correctly; however
it is documented incorrectly. The documentation says that this
function returns generators of the subgroup of K^x / (K^x)^m
consisting of elements a such that K(sqrt[m]{a})/K is unramified at
all primes of K lying above a place outside of S, However, this is not
true for the example given in the documentation!
sage: K.<a> = QuadraticField(-5)
sage: K.selmer_group((), 2)
[-1, 2]
sage: K.extension(x**2 - 2, 'b').relative_discriminant()
Fractional ideal (4)
The documentation should instead say that the output is the subgroup
consisting of all elements a such that the valuation v_p(a) is
divisible by m for any prime p not in S.
sage: K.<a> = QuadraticField(-5)
sage: K.selmer_group((), 2)
[-1, 2]
sage: ideal(K(2)).factor()
(Fractional ideal (2, a + 1))^2
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