2025 AMC 10A Problem 3

How many isosceles triangles are there with positive area whose side lengths are all positive integers and whose longest side has length 2025?

\textbf{(A)} 2025 \qquad \textbf{(B)} 2026 \qquad \textbf{(C)} 3012 \qquad \textbf{(D)} 3037 \qquad \textbf{(E)} 4050

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.