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Research Papers
On an elliptic curve defined over $\mathbb Q(\sqrt{-23})$
L. Dieulefaita, M. Minkb, B. Z. Morozc a Departament D'Álgebra i Geometria, Facultat de Matemátiques, Universitat de Barcelona, Barcelona, Spain
b Seminar für Mathematik und ihre Didaktik, Universität zu Köln, Köln, Germany
c Max-Planck-Institut für Mathematik, Bonn, Germany
Abstract:
Recently, the first three examples were found of elliptic curves without complex multiplication and defined over an imaginary quadratic field that have been proved to satisfy the Hasse–Weil conjecture. In the paper, the same algorithm is employed to prove the modularity and thereby the Hasse–Weil conjecture for the fourth elliptic curve without CM defined over the imaginary quadratic field $\mathbb Q(\sqrt{-23})$.
Keywords:
Hasse–Weil conjecture, elliptic curve.
Received: 10.07.2011
Citation:
L. Dieulefait, M. Mink, B. Z. Moroz, “On an elliptic curve defined over $\mathbb Q(\sqrt{-23})$”, Algebra i Analiz, 24:4 (2012), 64–83; St. Petersburg Math. J., 24:4 (2013), 575–589
Linking options:
https://www.mathnet.ru/eng/aa1292 https://www.mathnet.ru/eng/aa/v24/i4/p64
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Abstract page: | 426 | Full-text PDF : | 138 | References: | 65 | First page: | 24 |
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