COMPUTING ELLIPTIC CURVES OVER Q

被引：10
作者：
Bennett, Michael A. [1 ]
Gherga, Adela [1 ]
Rechnitzer, Andrew [1 ]
机构：
[1] Univ British Columbia, Dept Math, Vancouver, BC, Canada
来源：
MATHEMATICS OF COMPUTATION | 2019年 / 88卷 / 317期
基金：
加拿大自然科学与工程研究理事会;
关键词：
REDUCTION; CONDUCTOR; ALGORITHM; EQUATION; NUMBER;
D O I：
10.1090/mcom/3370
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We discuss an algorithm for finding all elliptic curves over Q with a given conductor. Though based on classical ideas derived from reducing the problem to one of solving associated Thue-Mahler equations, our approach, in many cases at least, appears to be reasonably efficient computationally. We provide details of the output derived from running the algorithm, concentrating on the cases of conductor p or p(2), for p prime, with comparisons to existing data.
引用
收藏
页码：1341 / 1390
页数：50
相关论文
共 69 条
[1]   ELLIPTIC-CURVES OF CONDUCTOR-11 [J].
AGRAWAL, MK ;
COATES, JH ;
HUNT, DC ;
VANDERPOORTEN, AJ .
MATHEMATICS OF COMPUTATION, 1980, 35 (151) :991-1002
[2]  
Akhtari S., AM J MATH
[3]  
[Anonymous], 1997, ALGORITHMS MODULAR E
[4]  
[Anonymous], LECT NOTES MATH
[5]   A fast algorithm to compute cubic fields [J].
Belabas, K .
MATHEMATICS OF COMPUTATION, 1997, 66 (219) :1213-1237
[6]  
BELABAS K., 1995, CMS C P, V20, P175
[7]  
Bennett M. A., CAIMS 2015 P
[8]   Mordell's equation: a classical approach [J].
Bennett, Michael A. ;
Ghadermarzi, Amir .
LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2015, 18 (01) :633-646
[9]  
Bernardin L., 2017, MAPLE PROGRAMMING GU
[10]   The Magma algebra system .1. The user language [J].
Bosma, W ;
Cannon, J ;
Playoust, C .
JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) :235-265
1234567