کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6415731 | 1335769 | 2011 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Rational torsion on optimal curves and rank-one quadratic twists
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Rational torsion on optimal curves and rank-one quadratic twists Rational torsion on optimal curves and rank-one quadratic twists](/preview/png/6415731.png)
چکیده انگلیسی
When an elliptic curve Eâ²/Q of square-free conductor N has a rational point of odd prime order lâ¤N, Dummigan (2005) in [Du] explicitly constructed a rational point of order l on the optimal curve E, isogenous over Q to Eâ², under some conditions. In this paper, we show that his construction also works unconditionally. And applying it to Heegner points of elliptic curves, we find a family of elliptic curves Eâ²/Q such that a positive proportion of quadratic twists of Eâ² has (analytic) rank 1. This family includes the infinite family of elliptic curves of the same property in Byeon, Jeon, and Kim (2009) [B-J-K].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 131, Issue 3, March 2011, Pages 552-560
Journal: Journal of Number Theory - Volume 131, Issue 3, March 2011, Pages 552-560
نویسندگان
Dongho Byeon, Donggeon Yhee,