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- W3036639462 abstract "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." @default.
- W3036639462 created "2020-06-25" @default.
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- W3036639462 date "2020-01-01" @default.
- W3036639462 modified "2023-09-28" @default.
- W3036639462 title "Rank zero elliptic curves induced by rational Diophantine triples" @default.
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- W3036639462 doi "https://doi.org/10.21857/m8vqrtq4j9" @default.
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