Arshdeep's ordered pairs

Find the total number of ordered pairs of integers (a,b) (a,b) satisfying

a2(b2+1)+b2(a2+16)=448. a^2 (b^2 + 1) + b^2(a^2 + 16) = 448.

This problem is shared by Arshdeep D, who came across it in Mathematical Mayham.

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