## 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 (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - 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 |