On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of \(rank\quad 3\). (English) Zbl 0606.14021

The authors give numerical evidence for the Birch Swinnerton-Dyer conjecture for a particular Weil curve whose Mordell-Weil group has rank 3. For the Weil curves of rank \(<3\) there is now very strong theoretical evidence for the Birch Swinnerton-Dyer conjecture, hence making a numerical investigation of a rank 3 curve very natural. The paper gives a very nice description of the mathematical preliminaries to the actual numerical calculation and ends by giving the numerical results which predict the Tate-Shafarevich group to be of order 1 up to 28 decimal places.
Reviewer: T.Ekedahl


14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14H45 Special algebraic curves and curves of low genus
14H52 Elliptic curves
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