Quantization Laguerre equation

Question

I saw this interesting article https://www.mdpi.com/2073-8994/14/4/741 about how the quantization of the eigenvalues of the Legendre equation is a consequence of parity symmetry and imposing that the solutions should be finite in the interval [-1,1]. I wonder if a similar argument could be made for the quantization of the eigenvalues of the Laguerre equation imposing that they don't blow up more rapidly than $e^x$. I'm aware that the Laguerre equation doesn't have parity symmetry. Does it have another symmetry (like translation symmetry)?