Am I in any place to ask for a lower car price when financing a new car?

My mom is getting me my first car and she has a credit score of 660. I wanted a 2016 Honda Civic coupe and on the internet price three days ago it was $19,000 then changed to 18,000 and now it's back up to 20,000. Because of my moms credit and no down payment, would we be able to negotiate the 18,000 again? Or lower?

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