Zero is neither positive nor negative. The concepts of positive and negative numbers are defined relative to zero, with negative numbers being less than zero and positive numbers being greater than zero.
Zero is an even number. It is an integer multiple of 2, and it satisfies the properties of being evenly divisible by 2 and fitting within the standard rules for sums and products of even numbers.
While zero was initially identified before the concepts of positive and negative numbers, it meets the formal definition of an even integer through being divisible by 2 with no remainder. Zero therefore has an even parity.