A non-rectangular trapezoid is called a Pepe Trapezoid if (a) it has integral side lengths, and (b) An ellipse that is not a circle with integral lengths of semi-major axis and semi-minor axis can be inscribed in the trapezoid such that the major axis or minor axis of the ellipse is perpendicular to the bases of the trapezoid. Prove or disprove that there are infinitely many non-similar Pepe trapezoids.