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The way to kill a supplied player base in the quickest time is to get about 6 or more battleships and shoot it for several hours. That is if it is a Core 1 base. You could kill it by yourself by making sure nobody can supply it by keeping the shield up. The shield uses the same amount of fuel when it is up no matter how much damage you do, so you just need to wait until the base runs out of fuel for the shield to go down.
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The well equipped ones have enough for several days, usually. The shields block 99% of incoming damage, so with enough consistent DPS hitting the base, it is possible to kill one.
Keeping the shield up also means the station can't be resupplied. Having a team of people keep the shields up around the clock would probably be the easiest way.