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Minimal models for 2-coverings of elliptic curves

Title data

Cremona, John E. ; Stoll, Michael:
Minimal models for 2-coverings of elliptic curves.
In: LMS Journal of Computation and Mathematics. Vol. 5 (2002) . - pp. 220-243.
ISSN 1461-1570
DOI: https://doi.org/10.1112/S1461157000000760

Abstract in another language

This paper concerns the existence and algorithmic determination of minimal models for curves of genus 1, given by equations of the form y2 = Q(x), where Q(x) has degree 4. These models are used in the method of 2-descent for computing the rank of an elliptic curve. The results described here are complete for unramified extensions of Q2 and Q3, and for all p-adic fields for p greater than or equal to 5. The primary motivation for this work was to complete the results of Birch and Swinnerton-Dyer, which are incomplete in the case of Q2. The results in this case (when applied to 2-coverings of elliptic curves over Q) yield substantial improvements in the running times of the 2-descent algorithm implemented in the program mwrank. The paper ends with a section on implementation and examples, and an appendix gives constructive proofs in sufficient detail to be used for implementation.

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
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 07:21
Last Modified: 12 Feb 2015 12:23
URI: https://eref.uni-bayreuth.de/id/eprint/6224