Buhler, Joe P.; Gross, Benedict H.; Zagier, Don B. On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of \(rank\quad 3\). (English) Zbl 0606.14021 Math. Comput. 44, 473-481 (1985). 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 Cited in 21 Documents MSC: 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 Keywords:order of Tate-Shafarevich group; Birch Swinnerton-Dyer conjecture; Weil curve × Cite Format Result Cite Review PDF Full Text: DOI