Debopam Chakraborty

activity

20182026

most citedConstruction of an infinite family of elliptic curves of 2-selmer rank 1 from heron triangles

3 citations · 4 across the 9 of their papers we have counts for

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10 papers · 1 filter

math.NT2026

Two infinite families of elliptic curves with Mordell-Weil rank at least $3$

Pankaj Patel, Debopam Chakraborty, Jaitra Chattopadhyay

In this paper, we consider two infinite parametric families of elliptic curves defined over $Q$ given by the equations $E_{a, b} : y^{2} = x^{3} - a^{2} x + b^{2}$ and $E^{\…

math.NT2025

Some bi-quadratic Pólya fields and large Pólya groups of compositum of simplest cubic and quintic fields

Md. Imdadul Islam, Debopam Chakraborty, Jaitra Chattopadhyay

The Pólya group $P o (K)$ of an algebraic number field $K$ is the subgroup of the ideal class group $C l_{K}$ generated by the ideal classes of the products of prime ideals of the sam…

math.NT2025

On the Mordell-Weil rank and $2$ -Selmer group of a family of elliptic curves

Pankaj Patel, Debopam Chakraborty, Jaitra Chattopadhyay

We consider the parametric family of elliptic curves over $Q$ of the form $E_{m} : y^{2} = x (x - n_{1}) (x - n_{2}) + t^{2}$ , where $n_{1}$ , $n_{2}$ and $t$ are particular…

math.NT2024

Bi-quadratic Pólya fields with five distinct ramified primes

Md. Imdadul Islam, Jaitra Chattopadhyay, Debopam Chakraborty

For an algebraic number field $K$ , the Pólya group of $K$ , denoted by $P o (K),$ is the subgroup of the ideal class group $C l_{K}$ generated by the ideal classes of the products of p…

math.NT2023

Large Pólya groups in simplest cubic fields and consecutive bi-qaudratic fields

Md. Imdadul Islam, Jaitra Chattopadhyay, Debopam Chakraborty

The Pólya group of an algebraic number field is the subgroup generated by the ideal classes of the products of prime ideals of equal norm inside the ideal class group. Inspired by…

math.NT2023

Heronian elliptic curves and the size of the $2$ -Selmer group

Debopam Chakraborty, Vinodkumar Ghale

A generalization of the congruent number problem is to find positive integers $n$ that appear as the areas of Heron triangles. Selmer group of a congruent number elliptic curve has…

math.NT2022

Class number divisibility of $Q (3 p, m - 21 p n^{2})$ constructed from elliptic curves of $2$ -Selmer rank exactly $1$

Debopam Chakraborty, Vinodkumar Ghale, MD Imdadul Islam

The class number divisibility problem for number fields is one of the classical problems in algebraic number theory, which originated from Gauss' class number conjectures. The rela…

math.NT2022★ 3 cited

Construction of an infinite family of elliptic curves of 2-selmer rank 1 from heron triangles

Debopam Chakraborty, Vinodkumar Ghale, Anupam Saikia

Given any positive integer n, it is well known that there always exist triangles with rational sides a, b and c such that the area of the triangle is n. Assuming finiteness of the…

math.NT2021★ 1 cited

Heron triangles and a family of elliptic curves with rank zero

Vinodkumar Ghale, Shamik Das, Debopam Chakraborty

Given any positive integer $n$ , it is well-known that there always exists a triangle with rational sides $a, b$ and $c$ such that the area of the triangle is $n$ . For a given prime…

math.NT2018

On a conjecture Mordell

Debopam Chakraborty, Anupam Saikia

A conjecture of Mordell states that if $p$ is a prime and $p$ is congruent to $3$ mod $4$ , then $p$ does not divide $y$ where $(x, y)$ is the fundamental solution to $x^{2}-py^{2}=1…