On the proportion of rank 0 twists of elliptic curves
A Dąbrowski - Comptes Rendus Mathematique, 2008 - Elsevier
Let E be an elliptic curve defined over Q, let Ed denote its dth quadratic twist, and [Formula:
see text]. We prove, that, for any positive integer k there are pairwise non-isogenous elliptic …
see text]. We prove, that, for any positive integer k there are pairwise non-isogenous elliptic …
[PDF][PDF] 椭圆曲线y2= x (x-2m)(x+ q-2m) 的非平凡奇数点
陈候炎 - 华中师范大学学报(自然科学版), 2010 - journal.ccnu.edu.cn
设m 是正整数, q 和q-2m 是奇素数. 本文运用初等数论方法证明了: 椭圆曲线y2= x (x-2m)(x+ q-
2m) 有适合2⫮ x 以及y≠ 0 的整数点(x, y) 的充要条件是: m> 2 且q= n2+(2m-2+ 1) 2, 其中n …
2m) 有适合2⫮ x 以及y≠ 0 的整数点(x, y) 的充要条件是: m> 2 且q= n2+(2m-2+ 1) 2, 其中n …
ON TWISTS OF THE FERMAT CUBIC x3 + y3 = 2
T Jedrzejak - International Journal of Number Theory, 2014 - World Scientific
We consider the Fermat elliptic curve E2: x3+ y3= 2 and prove (using descent methods) that
its quadratic twists have rank zero for a positive proportion of squarefree integers with fixed …
its quadratic twists have rank zero for a positive proportion of squarefree integers with fixed …
On several families of elliptic curves with arbitrary large Selmer groups
F Li, D Qiu - Science China Mathematics, 2010 - Springer
On several families of elliptic curves with arbitrary large Selmer groups Page 1 SCIENCE
CHINA Mathematics . ARTICLES . September 2010 Vol.53 No.9: 2329–2340 doi: 10.1007/s11425-010-4035-2 …
CHINA Mathematics . ARTICLES . September 2010 Vol.53 No.9: 2329–2340 doi: 10.1007/s11425-010-4035-2 …
A graphical method to calculate Selmer groups of several families of non-CM elliptic curves
F Li, D Qiu - arXiv preprint arXiv:0912.5072, 2009 - arxiv.org
arXiv:0912.5072v1 [math.NT] 27 Dec 2009 A graphical method to calculate Selmer groups of
several families of non-CM elliptic c Page 1 arXiv:0912.5072v1 [math.NT] 27 Dec 2009 A …
several families of non-CM elliptic c Page 1 arXiv:0912.5072v1 [math.NT] 27 Dec 2009 A …
ON POSITIVE PROPORTION OF RANK-ZERO TWISTS OF ELLIPTIC CURVES OVER
M Xiong - Journal of the Australian Mathematical Society, 2015 - cambridge.org
Extending the idea of Dabrowski ['On the proportion of rank 0 twists of elliptic curves', CR
Acad. Sci. Paris, Ser. I 346 (2008), 483–486] and using the 2-descent method, we provide …
Acad. Sci. Paris, Ser. I 346 (2008), 483–486] and using the 2-descent method, we provide …
On the Selmer groups and Mordell-Weil groups of elliptic curves over imaginary quadratic number fields of class number one
X Li - arXiv preprint arXiv:1207.0287, 2012 - arxiv.org
Let $ p $ and $ q $ be odd prime numbers with $ qp= 2, $ the $\varphi-$ Selmer groups,
Shafarevich-Tate groups ($\varphi-$ and $2-$ part) and their dual ones as well the Mordell …
Shafarevich-Tate groups ($\varphi-$ and $2-$ part) and their dual ones as well the Mordell …
[PDF][PDF] Arithmetic on a class of Jacobian varieties
A Dabrowski - mathevision.com
| III (E)|= 63, 4082. We consider the family E (n, p): y2= x (x+ p)(x+ p− 4· 32n+ 1) and its 2-
isogenous curves for p∈(Z\0)∩[− 1000, 1000] and n≤ 19. Compared to previously …
isogenous curves for p∈(Z\0)∩[− 1000, 1000] and n≤ 19. Compared to previously …