I'm trying to figure out how it is composed the RSA key. Follow what I know :
For a RSA 2048, 2048 is the bit length of the module.
The public key is composed by $(e,M)$ when $e$ is the public exponent and $M$ is the module.
The private key is composed by $(d,M)$ when $d$ is the private exponent and $M$ is the module.
Now, I tryed to find info about the standard bit lentght of the exponent without lack. Does anyone have info ? I need to define the max value that $d$ and $e$ can reach. I think that it useless to have the same exponent bit lenght of the module. Is it right ?