Did Pilate have Jesus executed?

How could Pilate have executed just Jesus and not rounded up others at the same time? The standard claim is that Pilate knew that if he extinguished the ringleader, the movement would cease (That worked out well, didn't it) History records what Pilate's second in command reported to him shortly after Jesus was executed.

However only one side of the conversation has been handed down through time.

'That Jesus business? All taken care of, as per your instructions.'

'Yes, there are groups of 500 plus Christians gathering together to say that their leader is still alive.'

'Do about it? Nothing, sir.'

'Their leader walks around Jerusalem freely. We could pick him up any time, but what would be the point?'

'But it isn't him, sir. It's his brother.'

'Somebody called James. No, I never heard of him either, sir.'

'He does look a lot like him, sir. It must be a family resemblance.'

'No sir, the public doesn't regard you as a laughing stock'.

'No sir, I can't see how anybody would regard your authority as undermined.'

'No sir, I am not incompetent. We picked up this Jesus guy and killed him, just as you said.'

'Of course it was the right guy. One of the gang members identified him.'

'No sir, it will never happen again sir.'

'Kill them all, sir? Yes sir, straight away sir.'