First, I know there are differences in logical qubits and physical qubits. It takes more physical qubits for each logical qubit due to quantum error.

Wikipedia states that it takes quantum gates of order $\mathcal{O}((\log N)^2(\log \log N)(\log \log \log N)$ using fast multiplication for Shor's Algorithm. That comes out to $1,510,745$ gates for $2^{1024}$. Further down the article, it says that it usually take $n^3$ gates for $n$ qubits. This would mean it would take ~$115$ qubits.

However, I've run Shor's Algorithm as implemented in Q# samples using Quantum Phase Estimation and it comes out to $1025$ qubits.