Computation of the Mordell-Weil Group

  • J. S. Chahal
Part of the The University Series in Mathematics book series (USMA)


If G is an abelian group (written additively), the elements g 1,..., g r of G are called independent if
$$m_1 g_1 + \cdots m_r g_r = 0\;\left( {m_j \varepsilon \mathbb{Z}} \right)$$
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 (E) of E is defined to be the maximum number of independent elements in E(ℚ). In particular, r (E) = 0 if and only if E(ℚ) is finite (consisting of points of finite order).


Elliptic Curve Rational Point Elliptic Curf Prime Divisor Integer Solution 
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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • J. S. Chahal
    • 1
  1. 1.Brigham Young UniversityProvoUSA

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