Should I Pay Charged Off Credit Card?

I just looked up my credit score and it's 587. Really low. I have 6 student loans and a credit card that my mother opened up in my name then she defaulted on it. Now I guess it's my job to pay it back. I owe 1,397 but it says "charged off" and the account is a negative account or something. Should I pay it back in one sum or in installments and will that improve my credit score?