Lugia is cause it's in the cover box but there are others as well like: Ho-oh, raiku, entei, suicune, zapdos, moltes, articuno, mewtwo, latios, and groudon (that's all i know and caught but there may be more)
In heart gold there is latias and kyogre and if you trade either kyogre or groudon you can get rayquaza
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there is no rarest Pokemon you have to train and train and including shinies there is no real rarest Pokemon at all.
no you can trade soulsilver pokemon to black
By far, they have said Celebi is the hardest/rarest Pokemon to obtain outside of Japan.
You CANNOT LEGALLY download Pokemon Soulsilver.
You'll need to trade for it from Pokemon HeartGold. It is not avilable in the wild in Pokemon SoulSilver.