Arkabrata Ghosh

works on

2-descent 1 elliptic curves 1 isogeny 1 rank zero 1 selmer groups 1 tate-shafarevich group 1

From the 1 of 7 linked papers with an AI index.

collaborators

7 papers

math.NT2026

Classification of the rank of a certain family of elliptic curves

Richa Sharma, Bidisha Roy, Arkabrata Ghosh

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

The paper determines exactly when the elliptic curves $y^{2} = x^{3} - pq x$ (with distinct odd prime parameters) have Mordell‑Weil rank zero and a trivial 2‑torsion part of the Tate–Sh…

math.NT2026

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

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

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…

math.NT2025

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…

Classification of the rank of a certain family of elliptic curves

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

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

Class groups of imaginary biquadratic fields

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

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

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 $y^{2} = x^{3} - m^{2} x + (pq r)^{2}$

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