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This conjecture is one of the seven **Millennium Prize Problems** listed by the **Clay Mathematics Institute**. This problem purely depends on **number theory and is widely recognized as most challenging problem**. This conjecture relates the arithmetic data associated to an elliptic curve E over a number field K to the behavior of the Hasse Weil L-function, ie L(E, s) of E at s = 1. So far this conjecture problem has not been proved and only special cases of the conjecture have been proved.

The problem was named after **Peter Swinnerton and Dyer** who in 1960's used computer at **University of Cambridge Computer Laboratory** developed the conjecture when trying to calculate the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known.

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