Izvorni znanstveni članak
https://doi.org/10.21857/m8vqrtq4j9
Rank zero elliptic curves induced by rational Diophantine triples
Andrej Dujella
orcid.org/0000-0001-6867-5811
; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
Miljen Mikić
orcid.org/0000-0003-4657-0642
; Kumičićeva 20, 51000 Rijeka, Croatia
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
Datum izdavanja:
15.9.2020.
Posjeta: 1.299 *