I'm particularly interested in the size of the elliptic, but also its eccentricity and whether it will be coplanar with Earth's ecliptic plane.
The orbit is more oval than elliptic since it is centered on... well, the center, rather than one focus. It is roughly perpendicular to the Sun-Earth axis. The orbital period 6 months. Radius of the orbit is 200,000km in the Z axis and 800,000km in the Y axis.
Sketch is very approximate, completely out of scale and meant to be conceptual, JWST only appears to orbit around L2 as an artifact of a rotating frame of reference. In an inertial frame of reference, it is in orbit around the Sun. And the Earth. Both at the same time, if you can wrap your head around that.