| Title:
|
Joint distribution for the Selmer ranks of the congruent number curves (English) |
| Author:
|
Vrećica, Ilija S. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
105-119 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We determine the distribution over square-free integers $n$ of the pair $(\dim _{\mathbb {F}_2}{\rm Sel}^\Phi (E_n/\mathbb {Q}),\dim _{\mathbb {F}_2} {\rm Sel}^{\widehat {\Phi }}(E_n'/\mathbb {Q}))$, where $E_n$ is a curve in the congruent number curve family, $E_n'\colon y^2=x^3+4n^2x$ is the image of isogeny $\Phi \colon E_n\rightarrow E_n'$, $\Phi (x,y)=(y^2/x^2,y(n^2-x^2)/x^2)$, and $\widehat {\Phi }$ is the isogeny dual to $\Phi $. (English) |
| Keyword:
|
elliptic curve |
| Keyword:
|
congruent number problem |
| Keyword:
|
Selmer group |
| MSC:
|
11G05 |
| MSC:
|
11N45 |
| MSC:
|
14H52 |
| idZBL:
|
07217123 |
| idMR:
|
MR4078348 |
| DOI:
|
10.21136/CMJ.2019.0171-18 |
| . |
| Date available:
|
2020-03-10T10:15:18Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148044 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Kane, D., Klagsbrun, Z.: On the joint distribution of $ Sel_\Phi (E/\mathbb{Q})$ and $ Sel_{\widehat{\Phi}}(E'/\mathbb{Q})$ in quadratic twist families.Available at https://arxiv.org/abs/1702.02687v1 (2007), 25 pages. |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
