It is commonly believed, even at the 101 university level, that distilled water has no ec, but pure distilled water(water that hasn't reacted with carbon dioxide) does have a low ec.
Once the atmoshpheric carbon dioxide reacts with water you have CO2 + H2O - H2CO3; Carbonic acid. Now you have a more recognizable and understood solution.
There are ways of removing the carbonic acid and raising the ph. You can also store it in glass containers to keep the water from reacting with carbon dioxide.