Second p-descents on elliptic curves

Title data

Creutz, Brendan:
Second p-descents on elliptic curves.
In: Mathematics of Computation. Vol. 83 (January 2014) Issue 285 . - pp. 365-409.
ISSN 0025-5718
DOI: https://doi.org/10.1090/S0025-5718-2013-02713-5

Abstract in another language

Let p be a prime and C a genus one curve over a number field k representing an element of order dividing p in the Shafarevich-Tate group of its Jacobian. We describe an algorithm which computes the set of D in the Shafarevich-Tate group such that pD = C and obtains explicit models for these D as curves in projective space. This leads to a practical algorithm for performing explicit 9-descents on elliptic curves over Q.

Further data

Item Type:	Article in a journal
Refereed:	Yes
Subject classification:	MSC (2010): Primary 11G05, 11Y50
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II 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:	12 Apr 2016 09:26
Last Modified:	12 Apr 2016 09:26
URI:	https://eref.uni-bayreuth.de/id/eprint/32173