Rank Conjecture Revisited
نویسنده
چکیده
The rank conjecture says that rank of an elliptic curve is one less the arithmetic complexity of the corresponding non-commutative torus. We prove the conjecture for elliptic curves E(K) over a number field K. As a corollary, one gets a simple estimate for the rank in terms of the length of period of a continued fraction attached to the E(K). As an illustration, we consider a family of elliptic curves with complex multiplication and a family of rational elliptic curves.
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