Something caught my attention while reading about the mathematics behind Elliptic Curve Cryptography.
When setting up the elliptic curve equation for communicating between parties, why are only the $a$ and $b$ variables altered, whereas the coefficients of $y^2$ and $x^3$ are kept constant at 1? Is there a specific reason behind or is it just standard?
Here is the general elliptic curve equation just in case: $y^2=x^3+ax+b$.