A conservative vector field has the property that the line integral of the vector field is independent of the path and depends only on the end points. This implies that the line integral of the vector field around a closed path is equal to zero. An equivalent property is that the curl of a conservative vector field is equal to zero. Also, the curl of the gradient of a scalar function is equal to zero. The electric field can be expressed as te gradient of a scalar electric potential.
There are enough different ways hinted at in the above paragraph that I'm sure you can easily prove that the electric field is conservative.