# What is the correct way to write the elastic net?

I am confused about the correct way to write the elastic net. After reading some research papers there seems to be three forms

1) $$\exp\{-\lambda_1|\beta_k|-\lambda_2\beta_k^2\}$$

2) $$\exp\{-\frac{(\lambda_1|\beta_k|+\lambda_2\beta_k^2)}{\sqrt{\sigma^2}}\}$$

3) $$\exp\{-\frac{(\lambda_1|\beta_k|+\lambda_2\beta_k^2)}{2\sigma^2}\}$$

I just don’t understand the correct way to add $$\sigma^2$$. Is any of the above expressions correct?