Computing the Mordell-Weil Group
A better title for this chapter might have been “Computing the Weak Mordell-Weil Group”, since we will be concerned solely with the problem of computing generators for the group E(K)/mE(K).However, given generators for E(K)/mE(K), a finite amount of computation will always yield generators for E(K). (See (VIII.3.2) and (exer. 8.18).) Unfortunately, there is no comparable algorithm currently known which is guaranteed to give generators for E(K)/mE(K)in a finite amount of time!
KeywordsExact Sequence Elliptic Curve Homogeneous Space Elliptic Curf Cohomology Class
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