Computing torsion points on curves.
Poonen, Bjorn (2001)
Experimental Mathematics
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Displaying similar documents to “Units from 3- and 4-torsion on jacobians of curves of genus 2”
Computing torsion points on curves.
The field of definition of the Mordell-Weil group of an elliptic curve over a function field
Masato Kuwata (1990)
Compositio Mathematica
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Abelian varieties and curves in
Dan Abramovich, Joe Harris (1991)
Compositio Mathematica
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Galois theory and torsion points on curves
Matthew H. Baker, Kenneth A. Ribet (2003)
Journal de théorie des nombres de Bordeaux
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In this paper, we survey some Galois-theoretic techniques for studying torsion points on curves. In particular, we give new proofs of some results of A. Tamagawa and the present authors for studying torsion points on curves with “ordinary good” or “ordinary semistable” reduction at a given prime. We also give new proofs of : (1) the Manin-Mumford conjecture : there are only finitely many torsion points lying on a curve of genus at least embedded in its jacobian by an Albanese map;...
The arithmetic-geometric mean and isogenies for curves of higher genus
Ron Donagi, Ron Livné (1999)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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No -torsion on elliptic curves over cubic number fields
Pierre Parent (2003)
Journal de théorie des nombres de Bordeaux
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We complete our previous determination of the torsion primes of elliptic curves over cubic number fields, by showing that is not one of those.
Torsion points on elliptic curves over all quadratic fields. II
Sheldon Kamienny (1986)
Bulletin de la Société Mathématique de France
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A Diophantine problem on algebraic curves over function fields of positive characteristic
J.F. Voloch (1991)
Bulletin de la Société Mathématique de France
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Hurwitz spaces of genus 2 covers of an elliptic curve.
Ernst Kani (2003)
Collectanea Mathematica
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Let E be an elliptic curve over a field K of characteristic not equal to 2 and let N > 1 be an integer prime to char(K). The purpose of this paper is to construct the (two-dimensional) Hurwitz moduli space H (E/K,N,2) which classifies genus 2 covers of E of degree N and to show that it is closely related to the modular curve X(N) which parametrizes elliptic curves with level-N-structure. More precisely, we introduce the notion of a normalized genus 2 cover of E/K and show that...