It’s hard to exclude genetics.
As far as a gene, several genes have been identified. In the end it will probably be a dozen genes interacting that lead toward the potential of high IQ.
As far as defining intellegence, it is like beauty, it’s hard to describe but you certainly know when you are stuck with ugly.
I would like to define it as a combination of short term memory capacity and brain processing speed. If you can hold a lot of info at once and manipulate it quickly, you are probably very smart.