Displaying similar documents to “P-division points on certain elliptic curves”

Quaternion Extensions of Order 16

Michailov, Ivo (2005)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12F12 We describe several types of Galois extensions having as Galois group the quaternion group Q16 of order 16. This work is partially supported by project of Shumen University.

Unramified quaternion extensions of quadratic number fields

Franz Lemmermeyer (1997)

Journal de théorie des nombres de Bordeaux

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Classical results of Rédei, Reichardt and Scholz show that unramified cyclic quartic extensions of quadratic number fields k correspond to certain factorizations of its discriminant disc k . In this paper we extend their results to unramified quaternion extensions of k which are normal over ℚ , and show how to construct them explicitly.

On equations defining fake elliptic curves

Pilar Bayer, Jordi Guàrdia (2005)

Journal de Théorie des Nombres de Bordeaux

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Shimura curves associated to rational nonsplit quaternion algebras are coarse moduli spaces for principally polarized abelian surfaces endowed with quaternionic multiplication. These objects are also known as . We present a method for computing equations for genus 2 curves whose Jacobian is a fake elliptic curve with complex multiplication. The method is based on the explicit knowledge of the normalized period matrices and on the use of theta functions with characteristics. As in the...