Reduction of elliptic curves over certain real quadratic number fields
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- by Masanari Kida PDF
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Abstract:
The main result of this paper is that an elliptic curve having good reduction everywhere over a real quadratic field has a $2$-rational point under certain hypotheses (primarily on class numbers of related fields). It extends the earlier case in which no ramification at $2$ is allowed. Small fields satisfying the hypotheses are then found, and in four cases the non-existence of such elliptic curves can be shown, while in three others all such curves have been classified.References
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Additional Information
- Masanari Kida
- Affiliation: Department of Mathematics, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan
- Email: kida@matha.e-one.uec.ac.jp
- Received by editor(s): January 31, 1997
- Received by editor(s) in revised form: January 2, 1998
- Published electronically: May 21, 1999
- Additional Notes: This research was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan.
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 1679-1685
- MSC (1991): Primary 11G05
- DOI: https://doi.org/10.1090/S0025-5718-99-01129-1
- MathSciNet review: 1654021