The theory of elliptic curves is one of the popular topics of recent times with its unsolved problems and interesting conjectures. In 1922, Mordell proved that the group of $\mathbb{Q}$-rational points on an elliptic curve is finitely generated. However, the rank of this group, signifying the number of independent generators, can be arbitrarily high for certain curves, a fact yet to be definitively proven. This study leverages the computer algebra system Magma to investigate curves with potentially high ranks using a technique developed by Mestre.
Primary Language | English |
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Subjects | Algebra and Number Theory |
Journal Section | Research Article |
Authors | |
Publication Date | June 30, 2024 |
Submission Date | April 10, 2024 |
Acceptance Date | May 23, 2024 |
Published in Issue | Year 2024 Issue: 47 |
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