On June 2nd and 3rd, 2019, 65 sprites were captured with a Phantom V2010 camera recording at 100,000 frames per second from Langmuir Laboratory (LL) in New Mexico. An extra sensitive slow-antenna known as LEFA, located 25 km east of LL, measured E-fields simultaneous with the video observations. Data from the Earth Networks Total Lightning Network (ENTLN) was used to locate their parent flash. By correlating all these datasets, we found the largest fraction of sprites with current signatures (45%) observed to date. These measured sprites have strong electromagnetic signatures comparable in magnitude to the largest current moments previously reported in the peer-reviewed literature, with range-normalized electric field changes of half the amplitude of their parent flashes, and current moments of up to 2742 kA km, as derived from a new computationally-efficient technique introduced here. Comparison to high-speed optical recordings shows also that optically-large sprites tend to have larger electrical currents.