As the formula give 1/6 of the gravitational potential energy is equal to alpha time 2 cos square of theta minus sin square of theta, having the lower quadripole energy means that the derivative of the second part of the equation must be equal to 0 but we have to check if it’s a minimum or a maximum of the function.
For alpha equal to 0, the equation will always be equal to 0 so the quadripole energy is constant.