Naslov
Rank zero elliptic curves induced by rational Diophantine triples

Autori
Dujella, Andrej ; Mikić, Miljen

Izvornik
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti (1845-4100) 24 (2020); 29-37

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Elliptic curves, Diophantine triples, rank, torsion group

Sažetak
Rational Diophantine triples, i.e. rationals a, b, c with the property that ab+1, ac+1, bc+1 are perfect squares, are often used in construction of elliptic curves with high rank. In this paper, we consider the opposite problem and ask how small can be the rank of elliptic curves induced by rational Diophantine triples. It is easy to find rational Diophantine triples with elements with mixed signs which induce elliptic curves with rank 0. However, the problem of finding such examples of rational Diophantine triples with positive elements is much more challenging, and we will provide the first such known example.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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