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.
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Keywords | elliptic curves
rank
biquadrates
sums of two biquadrates
parity conjecture
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Published Date | 2014-01
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Publication Title |
Mathematical Journal of Okayama University
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Volume | volume56
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Issue | issue1
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Publisher | Department of Mathematics, Faculty of Science, Okayama University
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Start Page | 51
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End Page | 63
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ISSN | 0030-1566
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NCID | AA00723502
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Content Type |
Journal Article
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language |
English
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Copyright Holders | Copyright©2014 by the Editorial Board of Mathematical Journal of Okayama University
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File Version | publisher
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Refereed |
True
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Submission Path | mjou/vol56/iss1/5
|
JaLCDOI |