Pratiksha Shingavekar

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20222025

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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 $φ$ . We give an upper and a l…

math.NT2024

Statistics for 3-isogeny induced Selmer groups of elliptic curves

Pratiksha Shingavekar

Given a sixth power free integer $a$ , let $E_{a}$ be the elliptic curve defined by $y^{2} = x^{3} + a$ . We prove explicit results for the lower density of sixth power free integers $a$ for w…

math.NT2024

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.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…

math.NT2024

An analogue of Kida's formula for elliptic curves with additive reduction

Anwesh Ray, Pratiksha Shingavekar

We study the Iwasawa theory of $p$ -primary Selmer groups of elliptic curves $E$ over a number field $K$ . Assume that $E$ has additive reduction at the primes of $K$ above $p$ . In t…

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

Statistics for 3-isogeny induced Selmer groups of elliptic curves

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

Rank distribution in cubic twist families of elliptic curves

An analogue of Kida's formula for elliptic curves with additive reduction

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