Conserved Quantity

A physical system in three spatial coordinates $$(x,y,z)$$ is described by the following Lagrangian:

$\large{L = x^2 \dot{y} + 2 z^3 \dot{x} \, \dot{y}^2 + 3 x \dot{x} \dot{z}}$

Which quantity must be conserved?

Details and Assumptions:
- The dot convention denotes time differentiation

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