Pratiksha Shingavekar

collaborators

5 papers

math.NT2025

A positive density of elliptic curves are diophantine stable in certain Galois extensions

Anwesh Ray, Pratiksha Shingavekar

Let $p \in {3, 5}$ and consider a cyclic $p$ -extension $L / Q$ . We show that there exists an effective positive density of elliptic curves $E$ defined over $ \mathbb{Q}…

math.NT2025

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning

Priyavrat Deshpande, Aditya Karnataki, Pratiksha Shingavekar

This article presents a comprehensive data-scientific investigation into the arithmetic statistics of congruent number elliptic curves, leveraging a dataset of square-free integers…

math.NT2025

$- 3$ -Selmer groups, ideal class groups and large $3$ -Selmer ranks

Somnath Jha, Dipramit Majumdar, Pratiksha Shingavekar

We consider the family of elliptic curves $E_{a, b} : y^{2} = x^{3} + a (x - b)^{2}$ with $a, b \in Z$ . These elliptic curves have a rational $3$ -isogeny, say $I ¨ $ . We give an upper and a…

math.NT2025

$3$ -Selmer group, ideal class groups and cube sum problem

Somnath Jha, Dipramit Majumdar, Pratiksha Shingavekar

Consider a Mordell curve $E_{a} : y^{2} = x^{3} + a$ with $a \in Z$ . These curves have a rational $3$ -isogeny, say $I ¨ $ . We give an upper and a lower bound on the rank of the $I ¨ $ -Selm…

math.NT2024

Rank distribution in cubic twist families of elliptic curves

Anwesh Ray, Pratiksha Shingavekar

Let $a$ be an integer which is not of the form $n^{2}$ or $- 3 n^{2}$ for $n \in Z$ . Let $E_{a}$ be the elliptic curve with rational $3$ -isogeny defined by $E_{a} : y^{2} = x^{3} + a$ , and $K…

A positive density of elliptic curves are diophantine stable in certain Galois extensions

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning

−3​-Selmer groups, ideal class groups and large 3-Selmer ranks

3-Selmer group, ideal class groups and cube sum problem

Rank distribution in cubic twist families of elliptic curves

$- 3$ -Selmer groups, ideal class groups and large $3$ -Selmer ranks

$3$ -Selmer group, ideal class groups and cube sum problem