Infinite descent on elliptic curves

被引：50
|
作者：
Siksek, S [1 ]
机构：
[1] UNIV EXETER, DEPT MATH, EXETER EX4 4QE, DEVON, ENGLAND
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 1995年 / 25卷 / 04期
关键词：
elliptic curves; Diophantine equations; computational number theory; Mordell-Weil group;
D O I：
10.1216/rmjm/1181072159
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present an algorithm for computing an upper bound for the difference of the logarithmic height and the canonical height on elliptic curves. Moreover, a new method for performing the infinite descent on elliptic curves is given, using ideas from the geometry of numbers. These algorithms are practical and are demonstrated by a few examples.
引用
收藏
页码：1501 / 1538
页数：38
相关论文
共 50 条
  • [21] Elliptic curves and continued fractions
    Igor V. Nikolaev
    Aequationes mathematicae, 2023, 97 : 219 - 229
  • [22] Orders of points on elliptic curves
    Shparlinski, IE
    AFFINE ALGEBRAIC GEOMETRY, 2005, 369 : 245 - 251
  • [23] Hypergeometric functions and elliptic curves
    Jeremy Rouse
    The Ramanujan Journal, 2006, 12 : 197 - 205
  • [24] Hypergeometric functions and elliptic curves
    Rouse, Jeremy
    RAMANUJAN JOURNAL, 2006, 12 (02): : 197 - 205
  • [25] SEQUENCES ASSOCIATED TO ELLIPTIC CURVES
    Gezer, Betul
    MATHEMATICAL REPORTS, 2022, 24 (04): : 821 - 847
  • [26] Elliptic curves and continued fractions
    Nikolaev, Igor V.
    AEQUATIONES MATHEMATICAE, 2023, 97 (02) : 219 - 229
  • [27] Dyadic torsion of elliptic curves
    Yelton J.
    European Journal of Mathematics, 2015, 1 (4) : 704 - 716
  • [28] Factoring numbers with elliptic curves
    Jorge Jiménez Urroz
    Jacek Pomykała
    The Ramanujan Journal, 2024, 64 : 265 - 273
  • [29] A normal form for elliptic curves
    Edwards, Harold M.
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 44 (03) : 393 - 422
  • [30] VARIATIONS ON TWISTS OF ELLIPTIC CURVES
    Ulas, Maciej
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2013, 43 (02) : 645 - 660
12345