papers

Publications (7)

math.NT2026

Modular curves of prime-power level with infinitely many quadratic points

Michael Cerchia, Rakvi

We completely determine the open subgroups of of prime-power level that satisfy and $\operatorname{det}(H)=\wideha…

math.NT2023

Serre curves relative to obstructions modulo 2

Jacob Mayle, Rakvi

We consider elliptic curves for which the image of the adelic Galois representation is as large as possible given a constraint on the image modulo 2. For su…

math.NT2026

The possible adelic indices for elliptic curves admitting a rational cyclic isogeny

Kate Finnerty, Tyler Genao, Jacob Mayle +1

In the 1970s, Serre proved that the adelic index of a non-CM elliptic curve over a number field is finite. More recently, Zywina conjectured the complete set of adelic indices for…

math.NT2023

On Possible Genus 0 adelic Galois Images of non CM Elliptic Curves over

Rakvi

Let be an elliptic curve defined over / Associated to , there is an adelic Galois representation $ρ_E \colon {\rm Gal}(\bar{\mathbb{Q}}/\mathbb{Q}) \to {\rm GL}…

math.NT2025

On possibilities of 3-adic Galois images associated to isogeny-torsion graphs

Rakvi

Let be a non CM elliptic curve defined over $\Q$. There is an isogeny-torsion graph associated to and there is also a Galois representation $ρ_{E,l^{\infty}} \colon \Gal(\…

math.NT2023

A Classification of Genus 0 Modular Curves with Rational Points

Rakvi

Let be a non-CM elliptic curve defined over . Fix an algebraic closure of . We get a Galois representation \[ρ_E \colon Gal(…