What things would I have to learn to understand the Birch and Swinnerton-Dyer Conjecture?

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Hopefully I'm accepted into grad. school this year—but, in the meantime, I've been lost as to what to study, outside of just going through textbooks.

I've decided to study a particular problem (I've found it difficult to find problems outside of being in school), and for this I'm trying to learn everything I can in order to understand the problem well. Hopefully, this will give me a bit more context, even if it necessitates going through textbooks (which I don't mind! I'm just struggling with direction.)

From reading it (the conjecture) I definitely want to further my studies in algebra?