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- W4289542801 abstract "While there has been considerable interest in the problem of finding elliptic curves of high rank over $mathbb{Q}$, very few parametrized families of elliptic curves of generic rank $geq 8$ have been published. In this paper we use solutions of certain symmetric diophantine systems to construct several parametrized families of elliptic curves with their generic ranks ranging from at least 8 to at least 12. Specific numerical values of the parameters yield elliptic curves with quite large coefficients and we could therefore determine the precise rank only in a few cases where the rank of the elliptic curve $leq 13$. It is, however, expected that the parametrized families of elliptic curves obtained in this paper would yield examples of elliptic curves with much higher rank." @default.
- W4289542801 created "2022-08-03" @default.
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- W4289542801 date "2018-09-18" @default.
- W4289542801 modified "2023-09-23" @default.
- W4289542801 title "Symmetric diophantine systems and families of elliptic curves of high rank" @default.
- W4289542801 doi "https://doi.org/10.48550/arxiv.1809.06603" @default.
- W4289542801 hasPublicationYear "2018" @default.
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