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ID 52068
FullText URL
Author
Izadi, F.A.
Khoshnam, F.
Nabardi, K.
Abstract
If an integer n is written as a sum of two biquadrates in two different ways, then the elliptic curve y2 = x3 − nx has positive rank. We utilize Euler’s parametrization to introduce some homoge- neous equations to prove that En has rank ≥ 3. If moreover n is odd and the parity conjecture is true, then the curve has even rank ≥ 4. Finally, some examples of ranks equal to 4, 5, 6, 7, 8 and 10, are also obtained.
Keywords
elliptic curves
rank
biquadrates
sums of two biquadrates
parity conjecture
Published Date
2014-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume56
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
51
End Page
63
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright©2014 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol56/iss1/5
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