Kukles revisited: Advances in computing techniques

We revisit the Kukles system to show how advances in computer hardware and software have improved symbolic calculations. We confirm directly that there are no non-persistent centres for the Kukles system. We also prove an earlier conjecture regarding the isochronous centres for the extended Kukles system. We introduce a technique whereby modular resultants can be used to investigate the properties of resultants that cannot be readily calculated using the existing software.