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Yes, these elastic constants are rather large. In fact, C11 is about 10^5 times larger than that of diamond, one of the stiffest known substances. If you look at the log file, you should be able to trace back to where C11 is calculated from the change in the Pxx component of the stress tensor when the box is alternately compressed and expanded by a small amount in the x direction. For a well-constructed calculation, the change in Pxx should be positive under compression and equal but opposite under expansion.
This calculation works well for simple crystals. For a complex structure like an amorphous polymer, a lot of issues arise, too numerous to mention here. Perhaps the best approach is to use the example ELASTIC_T, with a long equilibration time, and a fairly large (10%) strain magnitude, so that you can resolve the change in strain against the large amount of thermal noise.