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- W48436453 abstract "Let E be an elliptic curve over a number field K which satisfies the Taniyama-Weil conjecture for L E . The first assertion in the Birch and Swinnerton-Dyer conjecture is that L E(s) has a zero of order r = rk(E(K)). The rank of the Mordell-Weil group was the invariant of E that was completely inaccessible by elementary methods unlike, for example, the torsion subgroup of E(K). In the original papers where the conjecture was made, Birch and Swinnerton-Dyer checked the statement for a large family of curves of the form y 2 = x 3 — Dx and y 2 = x 3 — D, which, being curves with complex multiplication, have an L-function with analytic continuation." @default.
- W48436453 created "2016-06-24" @default.
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- W48436453 date "1987-01-01" @default.
- W48436453 modified "2023-09-23" @default.
- W48436453 title "Remarks on the Birch and Swinnerton-Dyer Conjecture" @default.
- W48436453 doi "https://doi.org/10.1007/978-1-4757-5119-2_18" @default.
- W48436453 hasPublicationYear "1987" @default.
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