Quadratic fields in Sage

Number fields - Constructions | Sage Reference Manual

SageMathCell

K = QuadraticField(2, 'x')
K.integral_basis()

[1, x]

K = QuadraticField(3, 'x')
K.integral_basis()

[1, x]

K = QuadraticField(5, 'x')
K.integral_basis()

[1/2*x + 1/2, x]

K = QuadraticField(7, 'x')
K.integral_basis()

[1, x]

K = QuadraticField(11, 'x')
K.integral_basis()

[1, x]

K = QuadraticField(13, 'x')
K.integral_basis()

[1/2*x + 1/2, x]

K = QuadraticField(17, 'x')
K.integral_basis()

[1/2*x + 1/2, x]

K = QuadraticField(19, 'x')
K.integral_basis()

[1, x]

K = QuadraticField(23, 'x')
K.integral_basis()

[1, x]