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Zapiski Nauchnykh Seminarov LOMI, 1979, Volume 82, Pages 5–28
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This article is cited in 2 scientific papers (total in 2 papers)
Orders of the torsion of points of curves of genus 1
V. A. Dem'yanenko
Abstract:
Let $K$ be an algebraic number field of degree $n$; $h(K)$ let be the number of divisor classes of the field $K$; $Y:v^2=u^4+au^2+b$ is the Jacobian curve over $K$; $b(a^2-4b)=c^2\prod^N_{i=1}q_i$ where $C$ is an integral divisor, $q_1,\dots,q_N$ are distinct prime divisors. One proves that there exists an effectively computable constant $c=c(n,h(K),N)$, such that the order $m$ of the torsion of any primitive $K$-point on $Y$ is bounded by it: $m\leqslant c$.
Citation:
V. A. Dem'yanenko, “Orders of the torsion of points of curves of genus 1”, Studies in number theory. Part 5, Zap. Nauchn. Sem. LOMI, 82, "Nauka", Leningrad. Otdel., Leningrad, 1979, 5–28; J. Soviet Math., 18:6 (1982), 843–861
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https://www.mathnet.ru/eng/znsl2090 https://www.mathnet.ru/eng/znsl/v82/p5
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Abstract page: | 141 | Full-text PDF : | 62 |
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