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.
Birincil Dil | İngilizce |
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Konular | Cebir ve Sayı Teorisi |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Yayımlanma Tarihi | 30 Haziran 2024 |
Gönderilme Tarihi | 10 Nisan 2024 |
Kabul Tarihi | 23 Mayıs 2024 |
Yayımlandığı Sayı | Yıl 2024 Sayı: 47 |
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