Mestre's Finite Field Method for Searching Elliptic Curves with High Ranks

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Journal of New Theory
Issue:47
Mestre's Finite Field Method for Searching Elliptic Curves with High Ranks

Mestre's Finite Field Method for Searching Elliptic Curves with High Ranks

Authors : Şeyda Dalkılıç, Ercan Altınışık

Pages : 20-27

Doi:10.53570/jnt.1467401

View : 128 | Download : 107

Publication Date : 2024-06-30

Article Type : Research Paper

Abstract :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.
Keywords : Mestre method, elliptic curve, rank, height matrix, magma

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