Pratiksha Shingavekar

activity

20222025

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

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

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4 papers · 1 filter

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★ 1 cited

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…