'"36V Lithium" battery, but no spec about how many kWh it stores.'
Speculating here…
They look like standard 18650 cells to me - they're readily available in both LiFePO4 and LiPo chemistries, but with 22 cells visible in the pictures, I'm guessing they're LiFePO4 because the nearest configuration to "36V" I can think of for 22 cells is 11S2P LiFePO4 cells at 35.2V, (the LiPo cells in 11S2P would be 40.7V nominal - a 10S LiPo would be "37V", but that doesn't make sense with 22 cells all up - maybe a 10S2P "motive" battery and an independant 2S pack to run the electronics?).
Typical LiFePO4 cells in 18650 size are 1350mAhr, so I'm guessing thats a 2.7Ahr @ 35.2V or a 95Wh - call it a 0.1kWh if you like. That seems a little low to get the indicated range/speeds quoted though - if you assume reasonable efficiency at half power, and that the bulk of power at top speed is aero drag, then the 250W used to ride at 25kmh would drop to doing only 19.5kmh at 125W (power going up with the cube of the speed thanks to the v squared term on the aero drag), so your 90Whr battery will only get you ~15km. If you halve the power again to 65W, and drop to 15kmh, you'd still only get a range of ~21km.
If they're LiPo cells though (with their increased fire risks), you can get inexpensively 2600mAhr cells in 18650 size - 22 of them (ignoring the difficulty in configuring a "36V" pack) gives you a bit over 210Whr - that'd still only give a 32km range @19kmh based on my assumptions above. Cells of 3000mAhr and over are around, they'd give you 244WHr and get maybe 40km @ 19kmh and _perhaps_ 50km @ 15kmh (but that'd take you 3 hours 20 mins)…
The "1000 cycle" battery life perhaps suggests LiPo instead of LiFePO4 (which is more commonly quites as "2000 cycles").
If I had to guess - I'd say it's a ~100Whr LiFePo4 pack at 35.2V, ad that the "50km" range relies on you providing over% of the motive power and travelling at a maximum of half top speed or so.
250w should get you close to 35kph on flat terrain. The limit is 25kph due to the legal laws not physical ones. The upside is it should be able to do 25kph up a steep hill just fine and there range numbers are reasonable. Edit: Ok, not all that steep a hill.
Hmmm - I've no good evaluation of this page's accuracy, but the first graph here says a 90kg bike/rider needs 250W to maintain 20kmh up only a 4% gradient hill. That's not very "steep". 20kmh up a 10% grade (which _is_ a "steep" hill) requires ~600W.
Speculating here…
They look like standard 18650 cells to me - they're readily available in both LiFePO4 and LiPo chemistries, but with 22 cells visible in the pictures, I'm guessing they're LiFePO4 because the nearest configuration to "36V" I can think of for 22 cells is 11S2P LiFePO4 cells at 35.2V, (the LiPo cells in 11S2P would be 40.7V nominal - a 10S LiPo would be "37V", but that doesn't make sense with 22 cells all up - maybe a 10S2P "motive" battery and an independant 2S pack to run the electronics?).
Typical LiFePO4 cells in 18650 size are 1350mAhr, so I'm guessing thats a 2.7Ahr @ 35.2V or a 95Wh - call it a 0.1kWh if you like. That seems a little low to get the indicated range/speeds quoted though - if you assume reasonable efficiency at half power, and that the bulk of power at top speed is aero drag, then the 250W used to ride at 25kmh would drop to doing only 19.5kmh at 125W (power going up with the cube of the speed thanks to the v squared term on the aero drag), so your 90Whr battery will only get you ~15km. If you halve the power again to 65W, and drop to 15kmh, you'd still only get a range of ~21km.
If they're LiPo cells though (with their increased fire risks), you can get inexpensively 2600mAhr cells in 18650 size - 22 of them (ignoring the difficulty in configuring a "36V" pack) gives you a bit over 210Whr - that'd still only give a 32km range @19kmh based on my assumptions above. Cells of 3000mAhr and over are around, they'd give you 244WHr and get maybe 40km @ 19kmh and _perhaps_ 50km @ 15kmh (but that'd take you 3 hours 20 mins)…
The "1000 cycle" battery life perhaps suggests LiPo instead of LiFePO4 (which is more commonly quites as "2000 cycles").
If I had to guess - I'd say it's a ~100Whr LiFePo4 pack at 35.2V, ad that the "50km" range relies on you providing over% of the motive power and travelling at a maximum of half top speed or so.