I had to make it request to join. We had 12 join that weren't from the forum, which isn't fair to you here. I will buy a diplomacy station to see it that allows me to send a link for you to request to join.
For how we can cooperate, the first way it to do "private" red star scans, which will be open to fellow members of the corporation. That way you don't have to rush to load orbs like some of the public missions.
Further options open up with diplomacy stations and trade stations, though I haven't made it that far.