Arman Shamsi Zargar and Naser Zamani

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 4, Pages 24–29

DOI: 10.7546/nntdm.2019.25.4.24-29

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## Details

### Authors and affiliations

Arman Shamsi Zargar

*Department of Mathematics and Applications, Faculty of Science
*

*University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran*

Naser Zamani

*Department of Mathematics and Applications, Faculty of Science
University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
*

### Abstract

We construct a subfamily of elliptic curves with , and show that its rank is at least five over . This improves the previous results on the rank of the curves over .

### Keywords

- Elliptic curves
- Independence
- Rank
- Torsion subgroup

### 2010 Mathematics Subject Classification

- 11G05
- 14H52

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## Cite this paper

APAZargar, A. S. & Zamani, N. (2019). A family of elliptic curves of rank ≥ 5 over ℚ(*m*). Notes on Number Theory and Discrete Mathematics, 25(4), 24-29, doi: 10.7546/nntdm.2019.25.4.24-29.

Zargar, Arman Shamsi and Naser Zamani. “A Family of Elliptic Curves of Rank ≥ 5 over ℚ(*m*).” Notes on Number Theory and Discrete Mathematics 25, no. 4 (2019): 24-29, doi: 10.7546/nntdm.2019.25.4.24-29.

Zargar, Arman Shamsi and Naser Zamani. “A Family of Elliptic Curves of Rank ≥ 5 over ℚ(*m*).” Notes on Number Theory and Discrete Mathematics 25.4 (2019): 24-29. Print, doi: 10.7546/nntdm.2019.25.4.24-29.