Rank zero elliptic curves induced by rational Diophantine triples (CROSBI ID 279828)
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Podaci o odgovornosti
Dujella, Andrej ; Mikić, Miljen
engleski
Rank zero elliptic curves induced by rational Diophantine triples
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.
Elliptic curves, Diophantine triples, rank, torsion group
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Podaci o izdanju
24
2020.
29-37
objavljeno
1845-4100
1849-2215
10.21857/m8vqrtq4j9
Povezanost rada
Matematika