Before creating your account bear in mind you'll need the bare minimum to register:
A valid academic or institutional e-mail address. Personal e-mail addresses will be evaluated on a case by case basis and may be subject to rejection
A real full name. Pseudonyms are not allowed
Information about your employer
A brief description of the intended use
Most Important: an SSH public key that you'l generate (prior to creating your account) as indicated
here
Use the signup on page to create (or administer) your account: https://xp.cortexlab.fr/app/signin.
Note that in order to access CorteXlab, you need to use ssh and you need to provide an ssh public key. Help on the SSH key generation.