Athena's rights are broad but follow a strict guideline as she is the goddess of knowledge, and needs to make sure her actions do not add or subtract knowledge from mortals. She has the rights to punish mortals with knowledge disablement, blindness, deafness, and lack of speech. More rights include teaching humans new inventions and determining who will win wars/battles, as shown in the Iliad and Odyssey, she helped craft the trojan horse, which won the battle for the Achaeans.
Athena has many more responsibilities than rights, as she gives mortals knowledge, but has to make sure she doesn't let them know too much or too little. Her additional responsibilities are; ~Protecting Athens from outside invaders, ~Protecting heroes on their quests as seen in the Odyssey helping Odysseus Hercules' labors and Perseus' beheading of Medusa and, ~helping humans with agriculture, as myths say that is was she who invented the plow and rake, the bridle, and how to yoke oxen to plow for mortals.