Aphids most often form clusters at the top of the basil plants as well as around the new growth. They suck sap from the plants and secrete a sticky, sweet solution that is relished by ants. You will often see ants farming aphids to harvest the secretions.
Artificial fertilizers promote lots of lush new growth. They may also weaken a plant's abilities to ward off attacks from pests. As long as the soil is fertile and contains plenty of organic matter, there should be no need to provide additional artificial nutrients to herbs such as basil. This will most likely also help prevent attacks by aphids and other pests.
Should an aphid attack occur, spraying the plants with a jet of water will sometimes eliminate the problem. If the aphids persist, insecticidal soap is a good choice. Use a commercial brand, or for a homemade solution, mix 2 tablespoons of liquid soap (not detergent) in a quart spray bottle. Spray the affected plants liberally, remembering to spray the undersides of the leaves as well.