| Title:
|
On a family of elliptic curves of rank at least 2 (English) |
| Author:
|
Chakraborty, Kalyan |
| Author:
|
Sharma, Richa |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
681-693 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $C_{m} \colon y^{2} = x^{3} - m^{2}x +p^{2}q^{2}$ be a family of elliptic curves over $\mathbb {Q}$, where $m$ is a positive integer and $p$, $q$ are distinct odd primes. We study the torsion part and the rank of $C_m(\mathbb {Q})$. More specifically, we prove that the torsion subgroup of $C_{m}(\mathbb {Q})$ is trivial and the $\mathbb {Q}$-rank of this family is at least 2, whenever $m \not \equiv 0 \pmod 3$, $m \not \equiv 0 \pmod 4$ and $m \equiv 2 \pmod {64}$ with neither $p$ nor $q$ dividing $m$. (English) |
| Keyword:
|
elliptic curve |
| Keyword:
|
torsion subgroup |
| Keyword:
|
rank |
| MSC:
|
11G05 |
| MSC:
|
14G05 |
| idZBL:
|
Zbl 07584095 |
| idMR:
|
MR4467935 |
| DOI:
|
10.21136/CMJ.2022.0106-21 |
| . |
| Date available:
|
2022-08-22T08:17:28Z |
| Last updated:
|
2024-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150610 |
| . |
| 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:
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| Reference:
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| Reference:
|
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| . |
