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Schaefer, Edward F. ; Stoll, Michael:
How to do a p-descent on an elliptic curve.
In: Transactions of the American Mathematical Society.
Bd. 356
(2004)
Heft 3
.
- S. 1209-1231.
ISSN 1088-6850
DOI: https://doi.org/10.1090/S0002-9947-03-03366-X
Abstract
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.
Weitere Angaben
| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Keywords: | Elliptic curve over number field; p-descent; Selmer group; Mordell-Weil rank; Shafarevich-Tate group |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik II (Computeralgebra) Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik II (Computeralgebra) > Lehrstuhl Mathematik II (Computeralgebra) - Univ.-Prof. Dr. Michael Stoll Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut |
| Titel an der UBT entstanden: | Nein |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 03 Feb 2015 07:38 |
| Letzte Änderung: | 14 Jan 2016 11:48 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/6228 |