| Title:
|
The Mordell-Weil bases for the elliptic curve $y^2=x^3-m^2x+m^2$ (English) |
| Author:
|
Rout, Sudhansu Sekhar |
| Author:
|
Juyal, Abhishek |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
1133-1147 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $D_m$ be an elliptic curve over $\mathbb {Q}$ of the form $y^2 = x^3 -m^2x +m^2$, where $m$ is an integer. In this paper we prove that the two points $P_{-1}=(-m, m)$ and $P_0 = (0, m)$ on $D_m$ can be extended to a basis for $D_m(\mathbb {Q})$ under certain conditions described explicitly. (English) |
| Keyword:
|
elliptic curve |
| Keyword:
|
Mordell-Weil group |
| Keyword:
|
canonical height |
| MSC:
|
11D59 |
| MSC:
|
11G05 |
| idZBL:
|
Zbl 07442479 |
| idMR:
|
MR4339116 |
| DOI:
|
10.21136/CMJ.2021.0238-20 |
| . |
| Date available:
|
2021-11-08T16:03:42Z |
| Last updated:
|
2024-01-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149243 |
| . |
| Reference:
|
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| Reference:
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