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

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)
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### References:

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