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- W4288088657 abstract "We describe a systematic investigation into the existence of congruences between the mod $p$ torsion modules of elliptic curves defined over $mathbb{Q}$, including methods to determine the symplectic type of such congruences. We classify the existence and symplectic type of mod $p$ congruences between twisted elliptic curves over number fields, giving global symplectic criteria that apply in situations where the available local methods may fail. We report on the results of applying our methods for all primes $pge7$ to the elliptic curves in the LMFDB database, which currently includes all elliptic curves of conductor less than ${500000}$. We also show that while such congruences exist for each $ple17$, there are none for $p geq 19$ in the database, in line with a strong form of the Frey-Mazur conjecture." @default.
- W4288088657 created "2022-07-28" @default.
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- W4288088657 date "2019-10-27" @default.
- W4288088657 modified "2023-09-26" @default.
- W4288088657 title "Global methods for the symplectic type of congruences between elliptic curves" @default.
- W4288088657 doi "https://doi.org/10.48550/arxiv.1910.12290" @default.
- W4288088657 hasPublicationYear "2019" @default.
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