Minimal Torsion in Isogeny Classes of Elliptic Curves
نویسندگان
چکیده
منابع مشابه
Explicit isogeny descent on elliptic curves
In this note, we consider an `-isogeny descent on a pair of elliptic curves over Q. We assume that ` > 3 is a prime. The main result expresses the relevant Selmer groups as kernels of simple explicit maps between finitedimensional F`-vector spaces defined in terms of the splitting fields of the kernels of the two isogenies. We give examples of proving the `-part of the Birch and Swinnerton-Dyer...
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We outline PARI programs which assist with various algorithms related to descent via isogeny on elliptic curves. We describe, in this context, variations of standard inequalities which aid the computation of members of the Tate-Shafarevich group. We apply these techniques to several examples: in one case we use descent via 9-isogeny to determine the rank of an elliptic curve; in another case we...
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Let Λ be a finite-dimensional associative algebra. The torsion classes of mod Λ form a lattice under containment, denoted by tors Λ. In this paper, we characterize the cover relations in tors Λ by certain indecomposable modules. We consider three applications: First, we show that the completely join-irreducible torsion classes (torsion classes which cover precisely one element) are in bijection...
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2 Elliptic Curves and Maps Between Them 2 2.1 The Group Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Weierstrass Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Maps Between Elliptic Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Dual Isogenies . . . . . . . . . . . . . . ....
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1994
ISSN: 0002-9947
DOI: 10.2307/2154714