In response to my query on an idea which is new idea on B.S.D conjecture ,i got a reply from various people,in that someone told me that proving the Tamagawa number conjecture for eigenforms of weight 2 ,will do it,can someone explain me clearly that how could one bridge the gap between elliptic curves,and modular forms by proving Tamagawa number conjecture for eigenforms of weight 2 , thanks a lot in advance
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The Tamagawa number conjecture is a generalization (due to Bloch and Kato, building on earlier work of Deligne and Beilinson) of the BSD conjecture. Proving the Tamagawa number for eigenforms of weight two is essentially the same thing as proving BSD for (modular, but all elliptic curves over $\mathbb Q$ are modular) elliptic curves.