Arkabrata Ghosh

activity

20242026

most citedOn the Family of Elliptic Curves

y^{2} = x^{3} - 5 pq x

1 citations · 1 across the 8 of their papers we have counts for

collaborators

8 papers

math.NT2026

Classification of the rank of a certain family of elliptic curves

Arkabrata Ghosh, Bidisha Roy, Richa Sharma

In this article, we study the family of elliptic curves $E_{- 2 pq} : y^{2} = x^{3} - 2 pq x$ , where $p$ and $q$ are distinct odd primes. Using a $2$ -isogeny methods and some elementary techniq…

math.NT2026

Exact classification of elliptic curves $y^{2} = x^{3} - pq x$ with rank $0$ and trivial $\Sha[2]$

Arkabrata Ghosh, Paul M. Voutier

For the elliptic curves $E_{p, q} : y^{2} = x^{3} - pq x$ where $p$ and $q$ are distinct odd primes, we establish necessary and sufficient conditions under which rank$\,E_{p,q}(\mathbb{Q}…

math.NT2025

Class groups of imaginary biquadratic fields

Kalyan Banerjee, Kalyan Chakraborty, Arkabrata Ghosh

We present two distinct families of imaginary biquadratic fields, each of which contains infinitely many members, with each member having large class groups. Construction of the fi…

math.NT2025

Rank of the family of elliptic curves $y^{2} = x^{3} - 5 p x$

Arkabrata Ghosh

This article considers the family of elliptic curves given by $E_{p} : y^{2} = x^{3} - 5 p x$ and certain conditions on an odd prime $p$ . More specifically, we have shown that if $p \equiv 7,…

math.NT2025★ 1 cited

On the Family of Elliptic Curves $y^{2} = x^{3} - 5 pq x$

Arkabrata Ghosh

This article considers the family of elliptic curves given by $E_{pq} : y^{2} = x^{3} - 5 pq x$ and certain conditions on odd primed $p$ and $q$ . More specifically, we have proved that if $p…

math.CO2024

The interplay between additive and symmetric large sets and their combinatorial applications

Arkabrata Ghosh, Sayan Goswami, Sourav Kanti Patra

The study of symmetric structures is a new trend in Ramsey theory. Recently in [7], Di Nasso initiated a systematic study of symmetrization of classical Ramsey theoretical results,…

math.NT2024

A necessary condition for $2 p$ to be congruent for a prime $p \equiv 5 (mod 8)$

Arkabrata Ghosh

In this article, we consider primes $p \equiv 5 (mod 8)$ and are able to prove that $p \equiv 5 (mod 16)$ if $2 p$ is a congruent number.

math.NT2024

On the family of elliptic curves $y^{2} = x^{3} - m^{2} x + (pq r)^{2}$

Arkabrata Ghosh

In this article, we consider a family of elliptic curves defined by $E_{m} : y^{2} = x^{3} - m^{2} x + (pq r)^{2}$ where $m$ is a positive integer and $p, q, and r$ are distinct odd…

Classification of the rank of a certain family of elliptic curves

Exact classification of elliptic curves y2=x3−pqx with rank 0 and trivial $\Sha[2]$

Class groups of imaginary biquadratic fields

Rank of the family of elliptic curves y2=x3−5px

On the Family of Elliptic Curves y2=x3−5pqx

The interplay between additive and symmetric large sets and their combinatorial applications

A necessary condition for 2p to be congruent for a prime p≡5(mod8)

On the family of elliptic curves y2=x3−m2x+(pqr)2

Exact classification of elliptic curves $y^{2} = x^{3} - pq x$ with rank $0$ and trivial $\Sha[2]$

Rank of the family of elliptic curves $y^{2} = x^{3} - 5 p x$

On the Family of Elliptic Curves $y^{2} = x^{3} - 5 pq x$

A necessary condition for $2 p$ to be congruent for a prime $p \equiv 5 (mod 8)$

On the family of elliptic curves $y^{2} = x^{3} - m^{2} x + (pq r)^{2}$