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Explicit isogeny descent on elliptic curves

Title data

Miller, Robert L. ; Stoll, Michael:
Explicit isogeny descent on elliptic curves.
In: Mathematics of Computation. Vol. 82 (2013) . - pp. 513-529.
ISSN 0025-5718
DOI: https://doi.org/10.1090/S0025-5718-2012-02619-6

Abstract in another language

In this note, we consider an ℓ-isogeny descent on a pair of elliptic curves over ℚ. We assume that ℓ > 3 is a prime. The main result expresses the relevant Selmer groups as kernels of simple explicit maps between finite-dimensional Fℓ-vector spaces defined in terms of the splitting fields of the kernels of the two isogenies. We give examples of proving the ℓ-part of the Birch and Swinnerton-Dyer conjectural formula for certain curves of small conductor.

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 28 Nov 2014 08:29
Last Modified: 28 Nov 2014 08:29
URI: https://eref.uni-bayreuth.de/id/eprint/4229