Swinnerton-Dyer Conjecture defence and neglection

Swinnerton-Dyer Conjecture In the early 1960s, B. Birch and H. P. F. Swinnerton-Dyer conjectured that if a given elliptic curve has an infinite number of solutions, then the associated L-series has value 0 at a certain fixed point. In 1976, Coates and Wiles showed that elliptic curves with complex multiplication having an infinite number of solutions have L-series which are zero at the relevant fixed point solution of mine mathmatics:-> if a given elliptic curve intesrsent with paraboal or hyperbola it cnat have infnity numebr of solutions,then associate lseries dt have value 0 at crtain fixed point even if we intersect by line with elliptic curve then Lseries have complex values as for intersent by parabola or hyperbola or single line

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