ID | 52068 |
フルテキストURL | |
著者 |
Izadi, F.A.
Mathematics Department, Azarbaijan Shahid Madani University
Khoshnam, F.
Mathematics Department, Azarbaijan Shahid Madani University
Nabardi, K.
Mathematics Department, Azarbaijan Shahid Madani University
|
抄録 | 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.
|
キーワード | elliptic curves
rank
biquadrates
sums of two biquadrates
parity conjecture
|
発行日 | 2014-01
|
出版物タイトル |
Mathematical Journal of Okayama University
|
巻 | 56巻
|
号 | 1号
|
出版者 | Department of Mathematics, Faculty of Science, Okayama University
|
開始ページ | 51
|
終了ページ | 63
|
ISSN | 0030-1566
|
NCID | AA00723502
|
資料タイプ |
学術雑誌論文
|
言語 |
英語
|
著作権者 | Copyright©2014 by the Editorial Board of Mathematical Journal of Okayama University
|
論文のバージョン | publisher
|
査読 |
有り
|
Submission Path | mjou/vol56/iss1/5
|
JaLCDOI |