The behavior of the Mordell-Weil group of elliptic curves. (English) Zbl 0741.14010

Brumer, Armand; McGuinness, Oisín

Bull. Am. Math. Soc., New Ser. 23, No. 2, 375-382 (1990).

The authors have calculated via computer the (predicted) Mordell-Weil rank of elliptic curves which are defined over the rational numbers and are selected to be of prime discriminant. Then they found a lot of elliptic curves of Mordell-Weil rank 2 and many interesting facts. From these results they confirm the computational evidence of several conjetures about the arithmetic theory of elliptic curves.

Reviewer: H.Maeda (Tokyo)

MSC:

14G40	Arithmetic varieties and schemes; Arakelov theory; heights
14Q05	Computational aspects of algebraic curves
14H52	Elliptic curves
11G40	\(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
11G05	Elliptic curves over global fields
14G10	Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)

Keywords:

Birch-Swinnerton-Dyer conjecture; Mordell-Weil rank of elliptic curves

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