Titlebook: Diophantine m-tuples and Elliptic Curves; Andrej Dujella Book 2024 The Editor(s) (if applicable) and The Author(s), under exclusive licens

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Diophantine m-tuples and Elliptic Curves978-3-031-56724-7Series ISSN 1389-2177 Series E-ISSN 2197-795X

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https://doi.org/10.1007/978-1-4612-1850-0. is discussed, with particular attention to those groups that can appear for curves induced by Diophantine triples. Methods for computing the rank and constructing elliptic curves with high rank are presented. The functions related to elliptic curves, available in the software package PARI/GP, are described.

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978-3-031-56726-1The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Sets with the Property ,blem is related to the distribution of ranks in families of twists of certain elliptic curves. Finally, we consider sets which are .-triples, quadruples and quintuples for several distinct values of .. Elliptic curves also play an important role here, but their appearance differs in those three problems.

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