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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A curve for which Coleman's effective Chabauty bound is sharp


Author: David Grant
Journal: Proc. Amer. Math. Soc. 122 (1994), 317-319
MSC: Primary 14H25; Secondary 14H40
MathSciNet review: 1242084
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Abstract: We show that Coleman's effective Chabauty bound is sharp for the curve $ C:{y^2} = x(x - 1)(x - 2)(x - 5)(x - 6)$ defined over $ \mathbb{Q}$, by considering its reduction $ \bmod\;7$. We also show that the Jacobian of C is absolutely simple.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1242084-4
PII: S 0002-9939(1994)1242084-4
Article copyright: © Copyright 1994 American Mathematical Society