Article
| 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 |
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| Category: | math |
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| 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 |
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| Date available: | 2022-08-22T08:17:28Z |
| Last updated: | 2022-12-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150610 |
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