Magma script for 'Diagonal quartic surfaces with a Brauer-Manin obstruction'.

R<T> := PolynomialRing(Integers());

K<i> := NumberField(T^2 +1);

A<x1,x2,y1> := AffineSpace(K,3);

I := ideal<CoordinateRing(A) |1 + x1^4 + x2^4 , y1^2 - (1 + i*x1^2)>;

C := Curve(A, I);

IsAbsolutelyIrreducible(C)