The olive branch is also a pretty neat aspect.
The myth is that Athena and Poseidon were competing to get the city named after them. Poseidon created either a spring or the first horse, depending on what version of the story we’re talking about. Athena gave them the first olive trees, which was a great hit amongst the people, so she won the contest.
So the coin not only reflects her with the owl, but also the gift of the olive they received from her.
The more modern belief though is that the city was named first, and Athena rose up as their mascot, since her name doesn’t really fit with typical naming conventions of the time, but moreso with the way places were named.

