I tracked Jupiter during its retrograde motion in the Spring and Summer of 2016, and used my usual fitting program to find the best values for its distance from the Sun at opposition and its angular speed , expressed as an instantaneous value of its period.  I can list those with the values I have found during previous oppositions:

Year          d (a.u.)             period (yrs)

2009   5.08 ± 0.10       11.1 ± 0.3

2010    4.95 ± 0.03       10.77 ± 0.08

2011     4.961 ± 0.006   10.81 ± 0.02

2015    5.328 ± 0.006  12.46 ± 0.03

2016   5.435 ± 0.003   12.92 ± 0.01

The first three distances are well below my measured value of 5.20 ± 0.02 for the semi-major axis, showing that Jupiter was somewhere close to perihelion, while the last two are nicely above it.  Jupiter is getting close to aphelion.  I hope I have sufficient information here  to pull out a good value for the eccentricity of the orbit.  For a quick and dirty value, I can combine the 2010 distance with my value for the semi-major axis to give an eccentricity of 0.048.