Click on the "Orbit" button on Heaven's Above and it shows the elset.

The orbit data is extracted from the following two-line orbital elements,

1 27647U 03003A 03023.25000000 .00062389 69891-5 12311-3 0 311
2 27647 39.0198 185.1824 0010531 47.7070 203.7036 15.99361520 1049

Epoch (UTC): 6:00:00 AM, Thursday, January 23, 2003
Eccentricity: 0.0010531
Inclination: 39.0198°
Perigee Height: 269 km
Apogee Height: 283 km
Right Ascension of Ascending Node: 185.1824°
Argument of Perigee: 47.7070°
Revolutions per Day: 15.99361520
Mean Anomaly at Epoch: 203.7036°
Orbit Number at Epoch: 104

I don't see anything really unusual about the orbit other than the 39 degree inclination. In the past, the Shuttle frequently launches into a 28.5 degree inclination unless it has a specific reason not to, such as going to the ISS or for a particular scientific purpose. I guess they had a specific reason for choosing a period of almost exactly 90 minutes.

As for the Shuttle appearing at almost the same time every day, that does seem surprising (it's doing it here, too). A sun synchronous orbit is specifically designed to do that, as is a Molynia orbit. Normal perturbation effects tend to shift the orbital plane every day. If you get the right combination of orbital altitude and inclination, then the perturbation effects serve to shift the orbital plane so that the satellite passes over the same place every day. It'll be interesting to review the elset in a few days and see how the RAAN has changed (or not).