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- W4221167579 abstract "In 2002 Watkins conjectured that given an elliptic curve defined over $mathbb{Q}$, its Mordell-Weil rank is at most the $2$-adic valuation of its modular degree. We consider the analogous problem over function fields of positive characteristic, and we prove it in several cases. More precisely, every modular semi-stable elliptic curve over $mathbb{F}_q(T)$ after extending constant scalars, and every quadratic twist of a modular elliptic curve over $mathbb{F}_q(T)$ by a polynomial with sufficiently many prime factors satisfy the analogue of Watkins' conjecture. Furthermore, for a well-known family of elliptic curves with unbounded rank due to Ulmer, we prove the analogue of Watkins' conjecture." @default.
- W4221167579 created "2022-04-03" @default.
- W4221167579 creator A5064835380 @default.
- W4221167579 date "2022-03-21" @default.
- W4221167579 modified "2023-09-26" @default.
- W4221167579 title "Watkins' conjecture for elliptic curves over function fields" @default.
- W4221167579 doi "https://doi.org/10.48550/arxiv.2203.10932" @default.
- W4221167579 hasPublicationYear "2022" @default.
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