Abstract
If G is an abelian group (written additively), the elements g 1,..., g r of G are called independent if
is possible only with m 1 = ⋯ = m r = 0. Thus if one of g 1,..., g r is of finite order, g 1,..., g r cannot be independent. For any elliptic curve E defined over ℚ the group E(ℚ) of rational points on E is finitely generated. The (Mordell-Weil) rank r ℚ(E) of E is defined to be the maximum number of independent elements in E(ℚ). In particular, r ℚ(E) = 0 if and only if E(ℚ) is finite (consisting of points of finite order).
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References
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© 1988 Springer Science+Business Media New York
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Chahal, J.S. (1988). Computation of the Mordell-Weil Group. In: Topics in Number Theory. The University Series in Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0439-3_7
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DOI: https://doi.org/10.1007/978-1-4899-0439-3_7
Publisher Name: Springer, Boston, MA
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