EUDML | A remark about isogenies of elliptic curves over quadratic fields

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Displaying similar documents to “A remark about isogenies of elliptic curves over quadratic fields”

Torsion points on elliptic curves over all quadratic fields. II

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Rational torsion points on elliptic curves over number fields

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The real field with the rational points of an elliptic curve

Ayhan Günaydın, Philipp Hieronymi (2011)

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We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets definable in that structure are semialgebraic.

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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Involutory elliptic curves over $𝔽_{q} (T)$

Andreas Schweizer (1998)

Journal de théorie des nombres de Bordeaux

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For $n \in 𝔽_{q} [T]$ let $G$ be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve $X_{0} (𝔫)$ . We determine all $𝔫$ and $G$ for which the quotient curve $G ∖ X_{0} (𝔫)$ is rational or elliptic.