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Construction of high-rank elliptic curves over ℚ and ℚ(t) with non-trivial 2-torsion

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Algorithmic Number Theory (ANTS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1122))

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Abstract

We construct a non-constant elliptic curve of rank at least 8, with a 2-torsion point, over the field ℚ(t 0, t 1, t 2, t 3, t 4).

By specializing the parameters to rational values, we obtain curves over ℚ with rational 2-torsion and of rank exactly 12, 13 and 14.

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Authors and Affiliations

  1. Université Denis Diderot-Paris 7, 2, place Jussieu, 75005, Paris, France

    Stéfane Fermigier

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  1. Stéfane Fermigier
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Henri Cohen

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© 1996 Springer-Verlag Berlin Heidelberg

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Fermigier, S. (1996). Construction of high-rank elliptic curves over ℚ and ℚ(t) with non-trivial 2-torsion. In: Cohen, H. (eds) Algorithmic Number Theory. ANTS 1996. Lecture Notes in Computer Science, vol 1122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61581-4_46

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  • DOI: https://doi.org/10.1007/3-540-61581-4_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61581-1

  • Online ISBN: 978-3-540-70632-8

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