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High-rank elliptic curves with given torsion group and some applications

Volume 126 / 2023

Andrej Dujella Banach Center Publications 126 (2023), 9-26 MSC: Primary 11G05; Secondary 11Y05 DOI: 10.4064/bc126-1


In this survey paper, we describe several methods for constructing elliptic curves with a given torsion group and high rank over the rationals and quadratic fields. We also discuss potential applications of such curves in the elliptic curve factorization method and their role in the construction of rational Diophantine sextuples.


  • Andrej DujellaDepartment of Mathematics
    Faculty of Science
    University of Zagreb
    Bijenička cesta 30
    10000 Zagreb, Croatia

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