The famous Da Vinci painting depicts Jesus and his 12 disciples during Jesus last meal, celebrating the Jewish passover.
It is customary to place a cup of wine in a goblet during passover, dedicated to the Prophet Elijah. (And kids are told that Elijah took a sip of the Wine, kind of like how Christian kids are taught about Santa Clause).
The Torah states that the Prophet has to appear before the Messiah, and according to Jewish Rabbi's the Prophet has yet to show.
IT IS NOT WHAT THE PAINTING SHOWS, BUT WHAT IT DOESNT SHOW.
It doesn't show the Goblet of Wine because Elijah WAS AT THE LAST SUPPER! That is why there is no Goblet on the Table, and why there is a Space on Jesus' right.
Regarding the "Cup of Christ", it would be an abomination of Judaism for there to be the Blood of Christ inside that Goblet. What Jesus was implying that he is of the Royal Bloodline of the House of David, and only through the House of David will the Messiah be from. (The Bible States that).
This is the underlying fact that separated Jews Vs. Christians. The Jews are still waiting for their Messiah, but they do not know that he already came to pass.
BTW: Regarding The Sign of the Fish that many Christians/Catholics have adopted, little do they know that it represents the Age of Pieces, indicating the Return and End of Days. We are currently leaving the House of Pieces and entering Aquarius within the next few years. The day of the Lord is soon.