Note on a circular cubic having one or more sextactic points at infinity
Haridas Bagchi, Biswarup Mukherji (1951)
Rendiconti del Seminario Matematico della Università di Padova
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Haridas Bagchi, Biswarup Mukherji (1951)
Rendiconti del Seminario Matematico della Università di Padova
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Hari das Bagchi, Manindra Chandra Chaki (1952)
Rendiconti del Seminario Matematico della Università di Padova
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Jun Ho Lee, Stéphane R. Louboutin (2014)
Acta Arithmetica
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Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic...
R. Conti (1990)
Annales Polonici Mathematici
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Bjorn Poonen (2001)
Journal de théorie des nombres de Bordeaux
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We prove that for any , the curve in is a genus curve violating the Hasse principle. An explicit Weierstrass model for its jacobian is given. The Shafarevich-Tate group of each contains a subgroup isomorphic to .
Čerin, Zvonko (2000)
Mathematica Pannonica
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Daniel F. Coray (1976)
Compositio Mathematica
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Isao Wakabayashi (2003)
Acta Arithmetica
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Yasutsugu Fujita, Tadahisa Nara (2015)
Acta Arithmetica
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We study integral points and generators on cubic twists of the Fermat cubic curve. The main results assert that integral points can be in a system of generators in the case where the Mordell-Weil rank is at most two. As a corollary, we explicitly describe the integral points on the curve.
P. Pleasants (1966)
Acta Arithmetica
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Hiroshi Ito (1989)
Journal für die reine und angewandte Mathematik
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