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I'm looking at soon studying some Elliptic Curves from Tate and Silverman's "Rational Points on Elliptic Curves" but I was wondering if knowing some algebraic geometry from Cox's "Ideals, Varieties and Algorithms" before reading Silverman's text would be a better approach or if I can just start learning elliptic curves right away.

Will understanding Algebraic Geometry at the level of "Ideals, Varieties and Algorithms" be sufficient for intuitive understanding in Silverman's Text "Rational Points on Elliptic Curves"?

In any case what would be the best approach?

As far as my background I know Abstract Algebra, Topology, slight amount of Number Theory, Linear Algebra, Real Analysis.

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  • $\begingroup$ Just go with the book. The theory of elliptic curves has its own taste, it is (also as a matter of taste) equally important to understand arithmetics (of the integers in number fields, the complicated $\Bbb Z$ is often enough), complex analysis, finite fields and their Galois theory, (co)homological tools, some sophisticated software like pari/gp and/or sage... (At that one point where Riemann-Roch is needed, just accept it.) Good luck! $\endgroup$ – dan_fulea May 30 '18 at 0:33
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Just try reading the Silverman's book, and if you find that you cannot follow, fall back to algebraic geometry fundamentals.

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