To calculate the minimum discrimination and the conductor of an elliptical curve using magma for example this elliptic curve, we use this command

E: = EllipticCurve ((0,8,0,48,0));

E;

Elliptical curve defined by y ^ 2 = x ^ 3 + 8 * x ^ 2 + 48 * x on the rational field

F: = MinimalModel (E);

F;

Elliptical curve defined by y ^ 2 = x ^ 3 – x ^ 2 + 2 * x – 2 on the rational field

D: = Discriminant (F);

N: = conductor (E);

My quastion is how to calculate the discriminant and the conductor when the curve has a variable coefficient for example this elliptical curve

$ y ^ 2 = x (x-a) (x-D ^ {p} zeta ^ {k}) $

Or $ a, D $ are integers and $ zeta ^ {k} $ is the k-th power of unity