The 3-isogeny selmer groups of the elliptic curves y2=x3+n2
Chan S. 2024. The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. International Mathematics Research Notices. 2024(9), 7571–7593.
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Abstract
Consider the family of elliptic curves En:y2=x3+n2, where n varies over positive cubefree integers. There is a rational 3-isogeny ϕ from En to E^n:y2=x3−27n2 and a dual isogeny ϕ^:E^n→En. We show that for almost all n, the rank of Selϕ(En) is 0, and the rank of Selϕ^(E^n) is determined by the number of prime factors of n that are congruent to 2mod3 and the congruence class of nmod9.
Publishing Year
Date Published
2024-05-01
Journal Title
International Mathematics Research Notices
Publisher
Oxford University Press
Acknowledgement
The author would like to thank Peter Koymans and Carlo Pagano for helpful discussions.
Volume
2024
Issue
9
Page
7571-7593
ISSN
eISSN
IST-REx-ID
Cite this
Chan S. The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. International Mathematics Research Notices. 2024;2024(9):7571-7593. doi:10.1093/imrn/rnad266
Chan, S. (2024). The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnad266
Chan, Stephanie. “The 3-Isogeny Selmer Groups of the Elliptic Curves Y2=x3+n2.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnad266.
S. Chan, “The 3-isogeny selmer groups of the elliptic curves y2=x3+n2,” International Mathematics Research Notices, vol. 2024, no. 9. Oxford University Press, pp. 7571–7593, 2024.
Chan S. 2024. The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. International Mathematics Research Notices. 2024(9), 7571–7593.
Chan, Stephanie. “The 3-Isogeny Selmer Groups of the Elliptic Curves Y2=x3+n2.” International Mathematics Research Notices, vol. 2024, no. 9, Oxford University Press, 2024, pp. 7571–93, doi:10.1093/imrn/rnad266.
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