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a is the square root of 3, as the coefficients of this matrix are defined on the number field with defining polynomial x^2 - 3, see:

sage: M.parent()
Full MatrixSpace of 2 by 2 dense matrices over Number Field in a with defining polynomial x^2 - 3 with a = 1.732050807568878?
sage: M
[ 1  0]
[ a -1]
sage: M[1,0]
a
sage: M[1,0]^2
3

a is the square root of 3, as the coefficients of this matrix are defined on the number field with defining polynomial x^2 - 3, see:

sage: M = s[2].canonical_matrix()
sage: M.parent()
Full MatrixSpace of 2 by 2 dense matrices over Number Field in a with defining polynomial x^2 - 3 with a = 1.732050807568878?
sage: M
[ 1  0]
[ a -1]
sage: M[1,0]
a
sage: M[1,0]^2
3