## Title data

Schaefer, Edward F. ; Stoll, Michael:

**How to do a p-descent on an elliptic curve.**

*In:* Transactions of the American Mathematical Society.
Vol. 356
(2004)
Issue 3
.
- pp. 1209-1231.

ISSN 1088-6850

DOI: https://doi.org/10.1090/S0002-9947-03-03366-X

## Abstract in another language

In this paper, we describe an algorithm that reduces the computation of the (full) p-Selmer group of an elliptic curve E over a number field to standard number field computations such as determining the (p-torsion of) the

S-class group and a basis of the S-units modulo pth powers for a suitable set S of primes. In particular, we give a result reducing this set S of ‘bad primes’ to a very small set, which in many cases only contains the primes above p. As of today, this provides a feasible algorithm for performing a full 3-descent on an elliptic curve over Q, but the range of our algorithm will certainly be enlarged

by future improvements in computational algebraic number theory. When the Galois module structure of E[p] is favorable, simplifications are possible and p-descents for larger p are accessible even today. To demonstrate how the

method works, several worked examples are included.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | Elliptic curve over number field; p-descent; Selmer group; Mordell-Weil rank; Shafarevich-Tate group |

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: | No |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 03 Feb 2015 07:38 |

Last Modified: | 14 Jan 2016 11:48 |

URI: | https://eref.uni-bayreuth.de/id/eprint/6228 |