Twists of Hessian Elliptic Curves and Cubic Fields

Katsuya Miyake

Displaying similar documents to “Twists of Hessian Elliptic Curves and Cubic Fields”

On a theorem of Mestre and Schoof

John E. Cremona, Andrew V. Sutherland (2010)

Journal de Théorie des Nombres de Bordeaux

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A well known theorem of Mestre and Schoof implies that the order of an elliptic curve $E$ over a prime field $𝔽_{q}$ can be uniquely determined by computing the orders of a few points on $E$ and its quadratic twist, provided that $q > 229$ . We extend this result to all finite fields with $q > 49$ , and all prime fields with $q > 29$ .

Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves

Aaron Levin (2007)

Journal de Théorie des Nombres de Bordeaux

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We study the problem of constructing and enumerating, for any integers $m, n > 1$ , number fields of degree $n$ whose ideal class groups have “large" $m$ -rank. Our technique relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.

A note on linear perturbations of oscillatory second order differential equations

Renato Manfrin (2010)

Archivum Mathematicum

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Under suitable hypotheses on $γ (t)$ , $λ (t)$ , $q (t)$ we prove some stability results which relate the asymptotic behavior of the solutions of $u^{''} + γ (t) u^{'} + (q (t) + λ (t)) u = 0$ to the asymptotic behavior of the solutions of $u^{''} + q (t) u = 0$ .

Projections of the twisted cubic

Joerg Meyer (2007)

The Teaching of Mathematics

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Siegel’s theorem and the Shafarevich conjecture

Aaron Levin (2012)

Journal de Théorie des Nombres de Bordeaux

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It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field $k$ and any finite set of places $S$ of $k$ , one can effectively compute the set of isomorphism classes of hyperelliptic curves over $k$ with good reduction outside $S$ . We show here that an extension of this result to an effective Shafarevich conjecture for of hyperelliptic curves of genus $g$ would imply an effective version of Siegel’s theorem for integral points...