If you "forget about" internal resistance, then the maximum current is infinite. An "ideal" component, non-existent in the real world, can provide mathematically "pure" infinite or zero amounts of resistance, voltage, current, and all the rest. Different battery compositions will have different amounts of real-world "impure" limitations.
Maximum Continuous Discharge Current This is the maximum current at which the battery can be discharged continuously. This limit is usually defined by the battery manufacturer in order to prevent excessive discharge rates that would damage the battery or reduce its capacity. Maximum 30-sec Discharge Pulse Current
This limit is usually defined by the battery manufacturer in order to prevent excessive discharge rates that would damage the battery or reduce its capacity. Maximum 30-sec Discharge Pulse Current This is the maximum current at which the battery can be discharged for pulses of up to 30 seconds.
If it lists the capacity as 50Ah at C/20 (common for lead-acid), that's 2.5A so you might want a better battery. EDT as Andy says, if your device draws bursts of higher current, you also need to know the max (not continuous, maybe called peak) discharge current of your battery matches whatever your load needs.
With a higher discharge current, of say 40A, the capacity might fall to 400Ah. In other words, by increasing the discharge current by a factor of about 7, the overall capacity of the battery has fallen by 33%. It is very important to look at the capacity of the battery in Ah and the discharge current in A.
The higher the internal resistance, the lower the maximum current that can be supplied. For example, a lead acid battery has an internal resistance of about 0.01 ohms and can supply a maximum current of 1000 amps. A Lithium-ion battery has an internal resistance of about 0.001 ohms and can supply a maximum current of 10,000 amps.