The multiple images of lensed quasars provide evidence on the mass distribution of the lensing galaxy .
The lensing invariants are constructed from the positions of the images , their parities and their fluxes .
They depend only on the structure of the lensing potential .
The simplest is the magnification invariant , which is the sum of the signed magnifications of the images .
Higher order configuration invariants are the sums of products of the signed magnifications with positive or negative powers of the position coordinates of the images .

We consider the case of the four and five image systems produced by elliptical power-law galaxies with \psi \propto ( x ^ { 2 } + y ^ { 2 } q ^ { -2 } ) ^ { \beta / 2 } .
This paper provides simple contour integrals for evaluating all their lensing invariants .
For practical evaluation , this offers considerable advantages over the algebraic methods used previously .
The magnification invariant is exactly B = 2 / ( 2 - \beta ) for the special cases \beta = 0 , 1 and 4 / 3 ; for other values of \beta , this remains an approximation , but an excellent one at small source offset .
Similarly , the sums of the first and second powers of the image positions ( or their reciprocals ) , when weighted with the signed magnifications , are just proportional to the same powers of the source offset , with a constant of proportionality B .
To illustrate the power of the contour integral method , we calculate full expansions in the source offset for all lensing invariants in the presence of arbitrary external shear .
As an example , we use the elliptical power-law galaxies to fit to the data on the four images of the Einstein Cross ( G2237+030 ) .
The lensing invariants play a role by reducing the dimensionality of the parameter space in which the \chi ^ { 2 } minimisation proceeds with consequent gains in accuracy and speed .