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A finiteness criterion for the number of rational points for twisted weil elliptic curves

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Abstract:

We consider the Weil elliptic curve E/ℚ and let $L(E,s) = \sum\nolimits_{n = 1}^\infty {a(n) n^{ - s} }$ be its canonical L-series. Admitting the Birch-Swinnerton-Dyer conjecture and fixing the curve E, a criterion is given for the finiteness of the group E_D(ℚ) for twisted elliptic curves E_D, defined by the condition

$L(E_D ,s) = \sum\nolimits_{n = 1}^\infty { \chi (n) a(n) n^{ - s} }$

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