It's an Ego T battery.
The Ego T batteries are the only EGo batteries with the 5-click enable/disable (and possibly only the Joye and Janty brand ones).
The latest Eastmall Riva 510 should also work with the Ego-T
tank atty and provide a it more heat (3.7v vs 3.4v). And the latest Eastmall-made Riva 510 SE batteries should have a 3-click enable/disable.
I think the 3-stage Ego clone should also work - not sure who makes it - it has no disable/enable but 5 clicks go between 3.2, 3.7 and 4.2 volts.
I don't think any of those would need a shorty 510 extender to fit the Ego-T
tank atomizer but some other Ego-alikes may need the extender (may have deeper threads and need the extender to connect electrically).
I cannot guarantee any of what I listed will work without the extender because I do not use
tank atomizers. And I cannot guarantee that they can use the same charger you have. I know real Joye/Joyetech brand Ego and Eastmall Riva 510 and the 3-stage Ego clone battery that I bought do all use the same charger.