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https://doi.org/10.21857/m8vqrtq4j9

Rank zero elliptic curves induced by rational Diophantine triples

Andrej Dujella orcid id orcid.org/0000-0001-6867-5811 ; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
Miljen Mikić orcid id orcid.org/0000-0003-4657-0642 ; Kumičićeva 20, 51000 Rijeka, Croatia


Puni tekst: engleski pdf 513 Kb

str. 29-37

preuzimanja: 427

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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 the 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.

Ključne riječi

Elliptic curves; Diophantine triples; rank; torsion group.

Hrčak ID:

243435

URI

https://hrcak.srce.hr/243435

Datum izdavanja:

15.9.2020.

Posjeta: 900 *