There's no way to tell for certain when you conceived as it can take up to a week after you ovulate, and if you don't track ovulation there's really no way to tell. That's why at the start of pregnancy doctors use your LMP to date pregnancy until you get a dating scan. If this is because of a paternity issue the only way to know for certain is to have a DNA test when baby is born.
Going by your last period, probably around June 5th. What's your due date? According to the conception calculator it should be late February.