Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

How to do a p-descent on an elliptic curve

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
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: 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