Excuse me, could you please clarify for me which "core coins" you are referring to specifically? Nonetheless, generally speaking, the major cryptocurrency exchanges, such as Binance, Coinbase, Kraken, and BitMEX, tend to list a wide range of popular and established coins. It's likely that if a coin is considered to be a "core" coin in the market, it would be listed on at least one of these exchanges, if not multiple. However, it's always a good idea to double-check the exchange's listings and trading pairs to ensure that the coin you're interested in is indeed available for trading.