Abstract
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!
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© 1986 Springer Science+Business Media New York
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Silverman, J.H. (1986). Computing the Mordell-Weil Group. In: The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol 106. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1920-8_11
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DOI: https://doi.org/10.1007/978-1-4757-1920-8_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-1922-2
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